Question

The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area is ______.

पर्याय

•  25 cm²

•  28 cm²

• 30 cm²

• 40 cm²

Answer 1

The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area is 30 cm².

In right angled triangle ABC having base 5 cm and hypotenuse 13 cm we are asked to find its area

Using Pythagorean Theorem

`AB^2 = AC^2 + BC^2`

Where, AB = hypotenuse = 13 cm, AC = Base = 5 cm, BC = Height

`(13)^2 = (5)^2 + BC^2`

`169 = 25 + BC^2`

`BC = sqrt( 169-25)`

BC = 12 cm  

Area of a triangle, say A having base 5 cm and altitude 12 cm is given by

`A = 1/2 (" Base" xx " Height ")`

Where, Base = 5 cm; Height = 12 cm

`A = 1/2 (5 xx 12)`

A = (5 × 6)

A = 30 cm²