Question

The length of the two sides of a right triangle containing the right angle differ by 2 cm. If the area of the triangle is 24xm^2, find the perimeter of the triangle.  

Answer 1

Given: Area of triangle `24cm^2`

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

`a-b=2cm` 

`a=2+b`               .............(1) 

Area of triangle =`1/2xxbxxh` 

⇒`24=1/2xxbxx(2+b)` 

⇒`48=b+1/2b^2` 

⇒`48=2b+b^2` 

⇒`b^2+2b-48=0` 

⇒`(b+8)(b-6)=0` 

⇒`b=-8  or  6`

Side of a triangle cannot e negative.

Therefore, b=cm 

Substituting the value of b=6 cm in equation (1), we get : 

`a=2+6=8cm` 

Now, `a=8cm, b=6cm` 
In the given right triangle we have to find third side. Using the relation 

`"(Hyp)"^2="(Oneside)"^2+"(otherside)"^2` 

⇒`Hyp^2=8^2+6^2` 

⇒`Hyp^2=64+36` 

⇒`Hyp^2=100` 

⇒`Hyp^2=10 cm`

So, the third side is 10 cm So,

perimeter of the triangle `a+b+c` 

=`8+6+10` 

=`24cm`