Question

The sides of a right angle triangle containing right angle are 5x centimetre and (3x-1) centimetre. If its area is 60 cm square, find its perimeter.

Answer 1

Area of triangle =(1/2)*base*height
60=(1/2)*5x*(3x-1)
15x²-5x-120=0
3x²-x-24=0
3x²-(9-8)x-24=0
3x²-9x+8x-24=0
3x(x-3)+8(x-3)=0
(x-3)(3x+8)=0

Roots of x are :3,-8/3
Since value of x cannot be negative so x=3

Base =5*3=15
Height =(3*3-1)=9-1=8

Using pythagorus theorem,
Hypotenuse ²=base²+height ²
Hyp²=15²+8²
Hyp²=225+64
Hyp²=289
Hyp=17

Perimeter of the triangle =hypotenuse +base +height
=17+15+8
=40 cm