Question

The area of right triangle is 150 cm square. if its altitude exceeds the base by 5 cm .calculate perimeter of triangle

Answer 1

Area of triangle =1/2*base*height
150=1/2*base*height
300=base*height.equation1
Also given
Base+5=height.. Equation 2
Put value of height from 2 in 1 we get
300=base*(base+5)
300=base²+5base
base²+5base-300=0
On solving we get
Base=15,-20
Side cannot be negative therefore base=15
And height =base+5=15+5=20
Therfore height =20
Perimeter of triangle =base+height+hypotenuse
Using phythagorus theorem we get
hypotenuse =(base²+height²) ^1/2
=(225+400)^1/2
=(625)^1/2
=25
Hypotenuse =25cm
Therefore perimeter =20+25+15=60cm