Question

The area of a right-angled triangle is 600 cm². If the base of the triangle exceeds the altitude by 10 cm, find all the three dimensions of the triangle.

Answer 1

Let the altitude of the triangle be x cm.

∴ Base = (x + 10) cm

Area of triangle = `1/2 xx "base" xx "height"`

`600 = 1/2 xx (x + 10) xx x`

600 × 2 = x(x + 10)

1200 = x² + 10x

x² + 10x – 1200 = 0

x² + 40x – 30x – 1200 = 0

x(x + 40) – 30(x + 40) = 0

(x + 40) (x – 30) = 0

x + 40 = 0

x = – 40

(Not possible)

x – 30 = 0

x = 30

∴ x = 30

Altitude x = 30 cm

Base = x + 10

= 30 + 10

= 40

H² = B² + P²

H² = (30)² + (40)²

H² = 900 + 1600

H² = 2500

H² = (50)²

H = 50

Hypotenuse = 50 cm