Consult: the oblique side of a right triangle is 15 cm long, and the sum of right angles is 20 cm. Find its area

Consult: the oblique side of a right triangle is 15 cm long, and the sum of right angles is 20 cm. Find its area

Using equation solution
Let the length of two right angles be x, y respectively
Then x 2 + y 2 = 15
x+y=20 (x+y)²=20² x²+2xy+y²=400 15²+2xy=400 xy=175/2 xy/2=175/4
So the area is 175 / 4

The length of the three sides of a right triangle is 15 cm 20 cm 25 cm. What is the area of this triangle?

A: the area of this triangle is 150 square centimeters

For a right triangle, the length ratio of three sides is 3; 4; 5. Given that the longest side is 15 cm, what is the area of this triangle?

From known
This triangle is a right triangle (according to Pythagorean theorem)
Side length of short right angle side: 15 △ 5 * 3 = 9 (CM)
Side length of long right angle side: 15 △ 5 * 4 = 12 (CM)
So the area of this triangle: 9 * 12 / 2 = 54 (cm ^ 2)
A: the area of this triangle is 56 square centimeters

The length of the three sides of a right triangle is 9,12,15 cm. What is the height of the hypotenuse?

Height = 9 × 12 △ 15 = 7.2 cm

Observe the following groups of data: (1) 8,15,17; (2) 7,12,15; (3) 12,15,20; (4) 7,24,25 A. 1 B. 2 C. 3 D. 4

① According to the Pythagorean theorem, the inverse theorem is a right triangle, so it is correct;
② 72 + 122 ≠ 152. The inverse theorem of Pythagorean theorem is not a right triangle, so it is wrong;
③ 122 + 152 ≠ 202. According to the Pythagorean theorem, the inverse theorem is not a right triangle, so it is wrong;
④ 72 + 242 = 252. The inverse theorem of Pythagorean theorem is a right triangle
Therefore, B

Judge whether the following groups of numbers can be used as the height of the three sides of a right triangle (1) 8,1,17 (2) 7,12,15 (3) 15,15,20 (4) 7,24,25

One
8 + 1 < 17, no
Two
7²=49
12²=144
15²=225
49 + 144 ≠ 225, no
Three
15²=225
20²=400
225 × 2 ≠ 400, no
Four
7²=49
24²=576
25²=625
49+576=625
The fourth group can

Determine whether the following groups of numbers can be used as the three sides of a right triangle【 What is the process of the first group?

（1）8,15,17.
8^2+15^2=17^2.
64+225=289.

Are three sides 7.24.25 right triangle

7²+24²=49+576=625=25²
It's a right triangle

If the ratio of the lengths of the two right angles of a right triangle is 3:4 and the length of the hypotenuse is 20, then the circumference of the triangle is______ .

∵ the ratio of the lengths of the two right angles of a right triangle is 3:4,
Let the length of two right angle sides be 3x, 4x,
∴（3x）2+（4x）2=202，
The solution: x = 4 or - 4
∴3x=12，4x=16，
The circumference of the triangle is: 12 + 16 + 20 = 48
So the answer is: 48

If the ratio of the two right sides of a right triangle is 3:4 and the length of the hypotenuse is 20, then its area is______ .

According to the meaning of the title, let the two right angles be 3x and 4x,
Then (3x) 2 + (4x) 2 = 202,
X = 4, so the two right angles are 12, 16;
One
2×12×16=96，
So its area is 96