Question

in a right angled triangle the smaller side are (x+9)cm and (2x+3)cm find its perimeter if area is 54cm

Answer 1

perimeter is 12+9+15
=36 cm

Answer 2

Given that,

The sides of a right angled triangles are (x+9) cm and (2x+3) cm.

Area, A = 54 cm²

To find,

The perimeter of a right angled triangle.

Solution,

Area of a right angled triangle is given by :

$A=\dfrac{1}{2}bh$

Let b = (x+9) cm and h = (2x+3) cm

So,

$54=\dfrac{1}{2}\times (x+9)\times (2x+3)\\\\108=2x^2+21x+27\\\\2x^2+21x-81=0$

It is a quadratic equation, x = 3

So, b = (x+9) cm = (3+9) cm = 12 cm

h = (2x+3) cm = 2(3) +3 = 9 cm

Let H is the hypotenuse of a triangle. Using Pythagoras theorem we get :

$H=\sqrt{12^2+9^2} =15\ cm$

The sum of all sides of a triangle is called its perimeter. So,

P = 12 + 9 + 15 = 36 cm