Question

The perimeter of a right angled triangle is 60 m and its hypotenuse is 26 cm then the area of the triangle is

• A. $120$ $c{m}^2$
• B. $121$ $c{m}^2$
• C. $119$ $c{m}^2$
• D. $125$ $c{m}^2$

Answer 1

The correct option is A $120$ $c{m}^2$

Given the perimeter of the right-angle triangle is 60 m and the hypotenuse is 26 cm

Let the base and height of the right-angle triangle is a and b cm

Then $a^2+b^2=(26{)}^2$

$\therefore a+b+\sqrt{a^2+b^2}=60\Rightarrow a+b+26=60\Rightarrow a+b=60-26\Rightarrow a+b=34$

$\therefore (a+b{)}^2=(34{)}^2\Rightarrow a^2+b^2+2ab=1156\Rightarrow 2ab=1156-(26{)}^2=1156-676=480\Rightarrow ab=240$

Then area of right angle triangle = $\frac{1}{2}ab=\frac{1}{2}\times 240=120c{m}^2$