Question

the hypotenuse of a right triangle is 25 cm . the difference between the other two sides of the triangle is 5cm . find the length of these sides​

Answer 1

Answer:

Length of shorter side =15cm

Length of longer side i= 20cm

Step-by-step explanation:

Let the length of the shorter side b x cm. Then, the length of the longer side = (x + 5) cm.

Since the triangle is right-angled, the sum of the squares of the sides must be equal to the square of the hypotenuse (Pythagoras Theorem).

x2 + (x + 5)2 = 2352

x2 + x2 + 10x + 25 = 625

2x2 + 10x - 600 = 0

x2 + 5x - 300 = 0

(x + 20) (x - 15) = 0

This gives x = 15 or x = - 20

We reject x = - 20 and take x = 15.

Thus, length of shorter side = 15 cm.

Length of longer side = (15 + 5) cm, i.e., 20 cm.