Question

The difference in the lengths of the altitude and the base of a right-angled triangle is 4 cm, and its hypotenuse is 20 cm. Find its perimeter.
(i) 24 cm (ii) 48 cm
(iii) 36 cm (iv) 16 cm​

Answer 1

Step-by-step explanation:

Let the base of the right triangle be x cm.

So, altitude = x + 4 cm

Hypotenuse = 20 cm

In a right triangle, square of the hypotenuse = sum of the squares of the other two sides

So, (20)² = (x)² + (x + 4)²

400 = x² + x² + 8x + 16

400 = 2x² + 8x + 16

384 = 2x² + 8x

x² + 4x - 192 = 0

(x² -12x) + (16x - 192) = 0

x (x - 12) + 16 (x - 12) = 0

(x + 16) (x - 12) = 0

x = -16 or x = 12

Since x refers to the length of a side, it cannot be negative.

So, x = 12 cm (base)

Altitude = x + 4 = 16 cm

Therefore, perimeter = Sum of three sides of the triangle = 12 + 16 + 20 = 48 cm

(ii) 48 cm