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It is known that the sum of the lengths of two sides of a triangle is 10, if the cosine of the angle between the two sides is exactly a root of the equation 2x & # 178; - 3x-2 = 0 Find the minimum perimeter of the triangle
From the equation, cos θ = - 1 / 2 or 2 (rounding) ∧ C ^ 2 = a ^ 2 + B ^ 2-2abcos θ = (a + b) ^ 2-ab.c ≥ 5 √ 5. A + B + C ≥ 10 + 5 √ 5
Given that the lengths of the two sides of a triangle are 4 and 5 respectively, and the cosine of their angle is the root of the equation 2x2 + 3x-2 = 0, then the length of the third side is ()
A. 20B. 21C. 22D. 61
Solve the equation 2x2 + 3x-2 = 0 to get x = - 2, or x = 12 ∵ the cosine of the angle θ between the two sides of the triangle is the root of the equation 2x2 + 3x-2 = 0, so cos θ = 12, then the length of the third side is 42 + 52 − 2.4.5.12 = 21, so choose B
If we know that the lengths of the two sides of a triangle are 4 and 5 respectively, and the cosine value of their angle is the root of the equation 2x square + 3x-2 = 0, then the length of the third side is
Just a moment
If the perimeter of the triangle is even, and the two sides are 2 and 7 respectively, the length of the third side should be______ ．
According to the trilateral relation of a triangle, it is obtained that the third side should be greater than 7-2 = 5 and less than 7 + 2 = 9, and the perimeter is even. If the known sum of two sides is 9, then the third side should be odd, so the third side should be equal to 7
It is known that the two sides of a triangle are 1 and 2 respectively, and the value of the third side is the root of the square of the equation 2x - 5 + 3 = 0
I'm in a hurry
The perimeter is 4.5
2x²－5＋3＝0
（x-1）（2x-3）=0
The solution is as follows
X = 1 or x = 3 / 2
Because the value of X is the third side of the triangle,
According to the sum of the two sides of the triangle is greater than the third side,
The difference between the two sides is less than that of the third side
We can see that x = 1 does not satisfy the condition,
We should give up
So x = 3 / 2
So the perimeter of the triangle is 1 + 2 + 3 / 2 = 4.5
Given that a.b.c. is the trilateral length of △ ABC, B.C satisfies (b-2) &# 178; + ic-3i = 0, and a is the solution of the equation ia-4i = 2, find the perimeter of △ ABC
Judging the shape of △ ABC
b=2
c=3
A = 2 or 6
When a = 2
2 + 2 is greater than 3
The triangle ABC is an isosceles triangle with a circumference of 7
When a = 6
If 2 + 3 is less than 6, it does not form a triangle
Let a, B, C be the trilateral length of △ ABC, B, C satisfy the square of | B-2 | + | C-3 | = 0, and a is the solution of the equation | x-4 | = 2, and find the perimeter of △ ABC
|X-4 | = 2X-4 = positive and negative, 2x = positive and negative 2 + 4x1 = 6, X2 = 2 | B-2 | + | C-3 | = 0 (b-2) square + | C-3 | = 0 (b-2) square ≥ 0, | C-3 | ≥ 0, so (b-2) square = 0, | C-3 | = 0, so B-2 = 0, C-3 = 0b = 2, C = 3, and because the sum of two sides is greater than the third side, if a = 6, then B + C = 2 + 3 = 5, a ≥ B + C
It is known that a, B and C are the side lengths of △ ABC, B and C satisfy (b-2) 2 + C − 3 = 0, and a is the solution of the equation | A-4 | = 2. Find the perimeter of △ ABC and judge the shape of △ ABC
∵ (b-2) 2 + | C-3 | = 0, ∵ B-2 = 0, C-3 = 0, ∵ B = 2, C = 3, ∵ A-4 | = 2, ∵ a = 6 or 2. When a = 6, B = 2, C = 3, it can not form a triangle. When a = 2, B = 2, C = 3, it is an isosceles triangle with perimeter of 7
Given that ABC is the side length of triangle ABC, BC satisfies (b-2) ^ 2 + / C-3 / = 0, and a is the solution of equation / x-4 / = 2, find the perimeter of triangle ABC
And judge the shape of the triangle
(b-2)^2+/c-3/=0
b=2
c=3
/x-4/=2
X = 6 (not rounding off)
x=2
Perimeter: 2 + 2 + 3 = 7
The shape of a triangle is an isosceles triangle
The perimeter of an isosceles triangle is 16cm. The middle line of a waist divides the triangle into two triangles with a perimeter difference of 2cm, and calculates the sides of the isosceles triangle
The vertex of the triangle is a, and the two waists are AB and AC respectively, so the bottom edge is BC, and the high Cd on the edge of ab. I won't draw the picture. I'll draw it myself,
Let AB = X,
So AB = AC = 2ad = 2dB
(1) If triangle ADC > triangle BDC, the following results can be obtained:
AD+AC+DC-(DB+BC+DC)=2
That is AD + AC + dc-ad-bc-dc = 2
So ac-bc = 2
That is BC = X-2
So the perimeter of triangle ABC = AB + AC + BC + 16
That is, x + X + X-2 = 16
X=6
The waist length is 6
(2) If triangle BDC > triangle ADC, we can get
DB+BC+DC-(AD+AC+DC)=2
That is DB + BC + dc-ad-ac-dc = 2
That is BC-AC = 2
That is BC = 2 + X
So the perimeter of triangle ABC = AB + AC + BC + 16
That is, x + X + X + 2 = 16
X=14/3
RELATED INFORMATIONS
- 1. The circumference of an isosceles triangle is 16cm, and each waist is 2cm longer than the bottom side?
- 2. On the number axis, there are x integers whose distance from the origin is less than, y negative integers whose absolute value is not greater than, and Z integers whose absolute value is 4. Find the value of X + y + Z
- 3. Seventh grade mathematics problem: if the absolute value of A-3 is known to be A-3, then A-3 = 0, and the value range of a is greater than or equal to 3. If the opposite number of A-3 - 3A + a = 0, find the value of A
- 4. Prove by mathematical induction that 1x4 + 2x7 + 3x10 +... + n (3N + 1) = n (n + 1) &# 178;,
- 5. In the sequence {an}, A1 = 1, a (n + 1) = 5 / 2-1 / an. Let BN = 1 / (An-2), find the general term formula of {BN} (2) let CN = - 3N * BN, find the sum of the first n terms of {cn}
- 6. How to calculate log2 ^ x * log2 ^ 2x = 2
- 7. What is the biggest difference between galvanized sheet with and without zinc flower?
- 8. How to calculate the weight of a 4 mm subway slab with a length of 10 meters and a width of 10 meters?
- 9. How to calculate the density of iron plate? Or how much is the density of iron plate?
- 10. 500 soldiers in a row. For the first time, 1, 2, 3, 4, 5 (1-5) from left to right; for the second time, 1, 2, 3, 4, 5, 6 (1-6) from right to left. How many soldiers reported 1 and 6?
- 11. It is known that the waist length of an isosceles triangle is three times the length of its base, and its circumference is 35 cm?
- 12. If the two sides of an isosceles triangle are 3 and 6, then the circumference of the isosceles triangle is () A. 12b. 15C. 12 or 15d. 18
- 13. If the two sides of an isosceles triangle are 2cm and 5cm in length, then its perimeter is______ ．
- 14. If the lengths of the two sides of an isosceles triangle are 4 and 6 respectively, find the height of the bottom edge
- 15. In △ ABC, a, B and C are sides, satisfying a & # 178; - AB BC AC = 0
- 16. In the acute triangle ABC, the lengths of three sides a, B and C are all integers, and a is less than B and less than C, a + B + C = 20
- 17. It is known that the lengths a, B and C of △ ABC are integers, and satisfy a > b > C, a = 7?
- 18. The lengths of three sides of triangle ABC are a, B, C, and a > b > C, ABC are positive integers, satisfying the condition of 1 / A + 1 / B + 1 / C = 1. Try to judge whether triangle ABC exists, and explain the reason
- 19. In the triangle ABC, the lengths of the three sides are a, B, C, a = n ^ 2-1, B = 2n, C = n ^ 2 + 1 (n is an integer greater than 1). Which side is right
- 20. The circumference of an isosceles triangle is known to be 20 (1) If the waist length is seven, the bottom length is (2) the bottom length is seven, and the waist length is (3) if the length of one side is seven, and the length of the other two sides is?