Question

The perimeter of a right triangle is 40 cm and its hypotenuse measures 17 cm. Find the area of the triangle.

Answer 1

The perimeter of a right triangle = 40 cm

Hypotenuse measures = 17 cm.

Let x and y are the another sides.

40 = 17 + x + y

x + y = 23

or y = 23 – y

So, we have 3 sides as x, 23-x and 17.

Apply Pythagoras theorem:

Hypotenuse² = Base² + Perpendicular²

17² = x² + (23-x)²

289 = x² + 529 + x² – 46x

x² – 23x + 120 = 0

(x – 8)(x – 15) = 0

x = 8 or x = 15

If x = 8 then y = 23-8 = 15

If x = 15 then y = 23-15 = 8

Now,

Area of triangle = 1/2 × base × height

= 1/2 × 8 × 15

= 60

Therefore, Area of triangle is 60 cm²