Question

The perimeter of a right triangle is 40 cm and its hypotenuse measure 17 cm. Find the area of the triangle. 

Answer 1

The perimeter of a right-angled triangle = 40 cm 

therfore,` a+b+c=40` 

Hypotenuse = 17 cm

Therefore, c = 17cm  

`a+b+c=40 cm` 

⇒`a+b+17=40` 

⇒` a+b=23` 

⇒`b=23-a `     .................(1) 

Now, using Pythagoras theorem, we have:     

`a^2+b^2=c^2` 

⇒ `a^2+(23-a)^2=17^2` 

⇒` a^2+529-46a+a^2=289` 

⇒` 2a^2-46a+529-289=0` 

⇒`2a^2-46a+240=0` 

⇒` a^2-23a+120=0` 

⇒`(a-15) (a-8)=0` 

⇒a=15  or  a=8 

Substituting the value of a=15, in equation (i) we get: 

`b=23-a` 

=`23-15` 

=`8 cm` 

If we had chosen 8, a cm, then, `b=23-8=15 cm` 

In any case, 

`"Area of triangle"=1/2xx"Base"xx"height"`  

=`1/2xx8xx15` 

=`60 cm^2`