Question

Perimeter of a right angled triangle is $40cm$ and length of its hypotenuse is $17cm$. The area of this triangle is

• A. 30 $c{m}^2$
• B. 60 $c{m}^2$
• C. 120 $c{m}^2$
• D. None of these

Answer 1

Answer: (B)

60 $c{m}^2$

$a+b+17=40$
$\Rightarrow a+b=23$
$a^2+b^2=289$
${(a-b)}^2=2(a^2+b^2)-{(a+b)}^2$
$=578-529=49$
$\Rightarrow a-b=7$
Solving, we get, a = 15cm, b = 8cm
Area of triangle $=\frac{1}{2}\times 15\times 8=60c{m}^2$