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