Question : The hypotenuse of a right-angled triangle is 39 cm and the difference of the other two sides is 21 cm. Then, the area of the triangle is:
Option 1: 270 cm2
Option 2: 450 cm2
Option 3: 540 cm2
Option 4: 180 cm2
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Correct Answer: 270 cm 2
Solution :
Let the two sides of the right-angled triangle as $a$ and $b$, where $a > b$.
Given that the hypotenuse is 39 cm and the difference of the other two sides is 21 cm.
$⇒a^2 + b^2 = 39^2$
$⇒a^2 + b^2 = 1521$ ____(i)
Also $a - b = 21$
$⇒a=21+b$
putting the value of $a$ in equation (i), we get,
$⇒(21+b)^2 + b^2 = 1521$
$⇒441+42b+2b^2-1521=0$
$⇒b^2+21b-540=0$
$⇒(b+36)(b-15)=0$
$⇒b=15$ cm
So, $a=21+b=21+15=36$ cm
$\therefore$ The area of a right-angled triangle = $ \frac{1}{2}$ × base × height = $\frac{1}{2}$ × 36 × 15 = 270 cm
2
Hence, the correct answer is 270 cm
2
.
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