Question

The difference between the sides at right angles in a right-angled triangle is 7 cm. The area of the triangle is 60 cm². Find its perimeter.

Answer 1

Area of the triangle 60cm^2

Let the sides of the triangle be a, b and c, where a is the height, b is the base and c is hypotenuse of the triangle. 

`a-b=7cm` 

`a=7+b`              ....................(1) 

Area of triangle `=1/2xxbxxh` 

⇒`60=1/2xxbxx(7+b)` 

⇒ `120=7b+b^2` 

⇒`b^2+7b+b^2` 

⇒`(b+15) (b-8)=0` 

⇒`b=-15  or  8` 

Side of a triangle cannot be negative.

Therefore, b = 8 cm.

Substituting the value of b = 8 cm, in equation (1):  

`a=7+8=15 cm` 

`Now, a=15 cm, b=8cm` 

Now, in the given right triangle, we have to find third side. 

`"(Hyp)"^2="(First side)"^2+"(Second side)"^2` 

⇒` Hyp^2` =`8^2+15^2` 

⇒`Hyp^2=64+225 ` 

⇒`Hyp^2=289` 

⇒`Hyp=17 cm` 

So, the third side is 17 cm.

Perimeter of a triangle = a + b + c.

Therefore, required perimeter of the triangle 15 + 8 + 1740 cm