In a right triangle whose three sides are integers, if the length of the oblique side is 5 and the area of the triangle is 6, then its perimeter is Completion

In a right triangle whose three sides are integers, if the length of the oblique side is 5 and the area of the triangle is 6, then its perimeter is Completion

a*b/2=6
ab=12
a^2+b^2=5^2
(a+b)^2-2ab=25
(a+b)^2=25+2ab=49
a+b=7
Perimeter = a + B + 5 = 12

The perimeter of the triangle is 10, and each side is an integer. What kind of triangle might this triangle be

The application of trilateral relation in triangle
In the same triangle, "the sum of any two sides is greater than the third side, and the difference between any two sides is less than the third side." this relationship is simple but useful
1. Judge whether a triangle can be formed by the length of three line segments
Three line segments of the following length can form a triangle ()
A.1cm,2cm,3cm B.1cm,4cm,2cm
C.2cm,3cm,4cm D.6cm,2cm,3cm
Analysis: from the sum of any two sides of the triangle is greater than the third side, choose C
Example 2. There are eight wooden sticks, their lengths are 1,2,3,4,5,6,7,8 respectively. If three of the eight wooden sticks are selected to form a triangle, the longest side of the triangle is required to be 8, and the difference between the other two sides is greater than 2, then the number of different triangles that can be formed is_________ .
Analysis: the other sides of the triangle can be: 7 and 4, 7 and 3, 7 and 2, 6 and 3, which can be combined into four different triangles
Because: and meet;
And meet the requirements;
And meet the requirements;
And satisfied
2. Find the third side by the condition of the length of the two sides of the triangle
If the lengths of three sides of a triangle are x, 2 and 3, then the value range of X is ()
A.B.C.D.
Analysis: from the triangle trilateral relationship, we can see that
Therefore, D
The lengths of two sides of a triangle are 3 and 8 respectively. If the third side is odd, the length of the third side is ()
A. 5 or 7 B.7 c.9 d.7 or 9
Analysis: let the length of the third side be X
Namely
If x is odd, it can only take 7 or 9, so D
3. The perimeter of a triangle is determined by the condition of the two sides of the triangle
If both sides of an isosceles triangle are 4cm and 9cm in length, then its circumference is________ cm.
Analysis: in an isosceles triangle, we know that the lengths of two sides are 4cm and 9cm respectively, so the third side can only be 4cm or 9cm. If we take 4cm, it does not conform to the trilateral relationship of the triangle, so if we take 9cm, its perimeter is 22cm
If the length of each side of a triangle is an integer and the sum of its two sides is 3, then the perimeter of the triangle is_________ .
Analysis: according to the meaning of the question, the length of the two sides should be 1 and 2. If the third side is x, then
That is, therefore
The perimeter is
4. Triangle trilateral relation and algebra knowledge combined application
If a, B and C are three sides of a triangle, then_________ .
Analysis: because a, B, C are the three sides of the triangle, so, that is
so
Given that a, B and C are the lengths of three sides, then the root of the equation is ()
A. There is no real root
B. There are two unequal positive real roots
C. There are two unequal negative real roots
D. Real roots with two different signs
Analysis: because
So a, B and C are all three sides of a triangle,
That is, and
Therefore, the equation has two unequal real roots
The sum of the two is, and the product of the two is
So the original equation has two unequal negative real roots
Choose C
The circumference of isosceles is 10 cm, the length of BC at the bottom is y cm, and the length of AB at the waist is x cm
(1) Write the function relation of Y with respect to X;
(2) Find the value range of X;
(3) Find the value range of Y
Analysis: (1)
(2) Because X and y are the sides of the triangle, so
Namely
According to the trilateral relationship of the triangle:
So,
That is, the value range of X is
(3) From this, we can get the following conclusions
therefore
Namely
So the value range of Y is