Question

The diffrence bwtween sides of right angle is 3 cm and its area is 54 cm^2 . Find its perimeter.

Answer 1

let the two sides be x and x+3
area = 54 cm2
1/2 (x) (x+3) =54
x2+3x = 2*54= 108
x2+3x -108 =0
(x+12 )(x-9) =0
x =9 cm

sides are 9 cm , 12cm
$h = \sqrt{{9}^{2} + {12}^{2} }$
$\sqrt{81 + 144}$
$\sqrt{225}$
15 cm
perimeter of triangle = 9+12+15
=36

Answer 2

let  x and x+3 be the sides of the triangle
area=54
using area formula 1÷2 ×b×h
1/2×x×x+3=54
x²+3x=108
using fractarisation
x=9:x=12
then the two sides are 9 and 12
 To find the hypo
ac²=ab²+bc²
ac²=9²+12²
ac=√225
=15
perimeter=a+b+c
9+12+15=36