Question

the length of the sides of a right angled triangle are 5x cam and (3x-1) cm. If the area of the triangle is 60 cm square find its semi perimeter

Answer 1

The figure above is the full solution

Answer 2

Given : The length of the sides forming a right angled triangle are 5x cm , (3x - 1) cm. the area of the triangle is 60 cm²..

To find : The semi perimeter of the triangle

solution : 5x and (3x - 1) are length of sides forming a right angled triangle.

then one side must be base and the other one must be altitude.

let base = 5x and then altitude = (3x - 1)

so, area of triangle = 1/2 base × altitude

⇒60 = 1/2 × 5x × (3x - 1)

⇒120 = 15x² - 5x

⇒24 = 3x² - x

⇒3x² - x - 24 = 0

⇒3x² - 9x + 8x - 24 = 0

⇒3x(x - 3) + 8(x - 3) = 0

⇒x = 3, -8/3 but x ≠ -8/3 as x is length

so x = 3

then base = 5 × 3 = 15 and altitude = 3x - 1 = 3 × 3 - 1 = 8

hypotenuse = √(15² + 8²) = 17

now semi perimeter = (15 + 8 + 17)/2

= 20

Therefore the semi perimeter of triangle is 20 cm