Question

the two legs of a right triangle are in the ratio (square root of 3)/2. if the hypotenuse is 10 units long, find the area of the triangle?

Answer 1

Dear Student,

◆ Answer -

Area = 24.74 sq.units

● Explanation -

Let x, y and z (hypotenuse) be sides of right angled triangle.

x/y = √3/2

x = √3y/2

For right angled triangle,

z^2 = x^2 + y^2

10^2 = (√3y/2)^2 + y^2

100 = 3y^2/4 + y^2

100 = 7y^2/4

y^2 = 100 × 4/7

y^2 = 400/7

y = 20/√7

Solve this for x,

x = √3y/2

x = √3/2 × 20/√7

x = 10√3/√7

Area of right angled triangle is -

A = 1/2 × x × y

A = 1/2 × 20/√7 × 10√3/√7

A = 24.74 sq.units

Hence, area of right angled triangle is 24.74 sq.units.

Best luck dear...