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Question

The lengths of the two sides of a right triangle containing the right angle differ by 2 cm. If the areah of the triangle is 24 cm2, find the perimeter of the triangle.


Solution

Let the base of the triangle be b cm and its height or perpendicular be p cm.

Given, p - b = 2  ... (1)

and area of triangle = 24 cm2 

12×b×p=24 ​​​​​​​

⇒ b×p=48​​​​​​​​​​​​​​

b=48p ​​​​​​​

On putting the value of b in (1), we get

p48p=2 ​​​​​​​

p22p48=0 ​​​​​​​

⇒ p28p+6p48=0 ​​​​​​​

(p8)(p+6)=0 ​​​​​​​

⇒ p=8,6 ​​​​​​​

p ≠ -6. So, p = 8 cm

On putting p in (1), we get

⇒ b = 6 cm

So, Hypotenuse (h) =p2+b2=82+62=64+36=100=10 ​​​​​​​   ​​​​​​​

Hence, perimeter of triangle = p + b + h = 8 cm + 6 cm + 10 cm = 24 cm

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