Question

The length of the hypotenuse of a right-angled triangle exceeds the length of the base by 2 cm and exceeds twice the length of the altitude by 1 cm. Find the length of each side of the triangle.

Answer 1

Let the base and altitude of the right-angled triangle be x and y cm, respectively 

Therefore, the hypotenuse will be (x + 2) cm.

∴ (x + 2)² = y² + x²........(i)

Again, the hypotenuse exceeds twice the length of the altitude by 1 cm.

∴ h = (2y + 1)

⇒ x + 2 = 2y + 1

⇒ x = 2y - 1

Putting the value of x in (i), we get:

Thus, the base, altitude and hypotenuse of the triangle are 15 cm, 8 cm and 17 cm, respectively.