Question

The area of triangle is 54cm^2 the difference between the side is right angle is 3cm find its perimeter

Answer 1

Let's consider Base as b and Height as h,


(1/2) x b x h = 54

b x h = 108 .......(1)

We know that,

b - h = 3

Now after multiplying both sides by b we get,

(b x b) - (b x h) = (3 x b)

b² - 108 = 3b ....... since b x h = 108

b² - 3b - 108 = 0

After solving this we get,

b = 12

Putting this in eq(1),

12 x h = 108

h = 9

So now we have b = 12 and h = 9. We'll need to find third side in order to find perimeter.

So using Pythagoras Theorem we get third side as 15.

12² + 9² = c²

c² = 225

c = 15

Perimeter of triangle = b + h + c
= 12 + 9 + 15
= 36