Question

The legs of a right-angled triangle are in the ratio 4 : 3 and its area is 4056 cm². Find the length of its legs.

Answer 1

Area of right-angled triangle = 4056 cm²

Legs of a right-angled triangled are in the ratio i.e. 4 : 3

Let one leg (Base) = 3x

Then second leg (altitude) = 4x

Area =`1/2xx"Base"xx"Altitude"`

= `1/2xx3"x"xx4"x"` = 6x²

∴ 6x² = 4056

x² = `4056/6` = 676

x = `sqrt676=sqrt(26xx26)`

∴ x = 26 cm

∴ One leg (base) = 3x = 3 × 26 = 78 cm

and second leg (altitude) 4x = 4 × 26 = 104 cm