Question : The perimeter of a right triangle is 60 cm and its hypotenuse is 26 cm. What is the area (in cm2) of the triangle?
Option 1: 60
Option 2: 96
Option 3: 90
Option 4: 120
Correct Answer: 120
Solution :
The perimeter of a right triangle = 60 cm
And hypotenuse = 26 cm
In right angle triangle,
$\text{hypotenuse} ^2$ = $\text{base} ^2$ + $\text{perpendicular}^2$
Let the base be $x$, then the perpendicular = (60 – 26) – $x$ = (34 – $x$) cm.
So, $x^2+(34-x)^2=26^2$
⇒ $2x^2-68x+1156-676=0$
⇒ $x^2-34x+240=0$
⇒ $(x-24)(x-10)=0$
⇒ $x=24$ or $x=10$
Therefore, base length= 10 cm or 24 cm
And perpendicular length = 24 cm or 10 cm
Now area of triangle = ($\frac{1}{2}$) × 10 × 24 = 120 cm
2
Hence, the correct answer is 120.
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