Question

The area of a right-angled triangle is 40 sq cm and its perimeter is 40 cm. The length of its hypotenuse is:
(a) 16 cm
(b) 18 cm
(c) 17 cm
(d) data insufficient

Answer 1

Given :-

The area of a right-angled triangle is 40 sq cm and its perimeter is 40 cm

To Find :-

Length of hypotenuse

Solution :-

Area of a right-angled triangle = 1/2 × b × h

40 = 1/2 × a × b

40 × 2 = ab

80 = ab (i)

Let the hypotenuse be x

Perimeter = a + b + c

40 = a + b + x

40 - x = a + b

On squaring both sides

(40 - x)² = (a + b)²

As we know,

• (a - b)² = a² - 2ab + b²
• (a + b)² = a² + 2ab + b²

(40)² - 2(40)(x) + (x)² = a² + 2ab + b²

1600 - 80x + x² = a² + 2ab + b²

From 1

1600 - 80x + x² = a² + 2(80) + b²

1600 - 80x + x² = a² + 160 + b²

• a² + b² = x²

1600 - 80x + x² = x² + 160

Cancel x²

1600 - 80x = 160

1600 - 160 = 80x

1440 = 80x

1440/80 = x

18 = x

Option B is correct.