# The hypotenuse of a right-angled triangle is 39 cm :

The hypotenuse of a right-angled triangle is 39 cm and the difference of other two sides is 21 cm. Then the area of the triangle is

1. 450 sq. cm
2. 540 sq. cm
3. 180 sq. cm
4. 270 sq. cm
Anurag Mishra Professor Asked on 29th December 2015 in

Answer is 270 sq. cm

Explanation:-

The hypotenuse of a right-triangle = 39 cm

The difference of other two sides = 21 cm
Let one side be X cm and another side be X – 21 cm.

As we know that, the square of both side = the square of hypotenuse.
Then, X2 + (X – 21)2  = 392
X2 + X2 + 212 – 2 x 21 X = 39 x 39
2 X2 + 441 – 42 X = 1521
2 X2 + 441 – 42 X – 1521 = 0
2 X2 – 42 X – 1080 = 0
2 X2 – 72 X + 30 X – 1080 = 0
2 X (X – 36) + 30 (X – 36) = 0
(X – 36) (X + 30) = 0
X – 36 = 0
X = 36

Then, the other two sides are X = 36 cm and X – 21 = 36 – 21 = 15 cm

So, the area of the triangle = 36 x 15/2
= 18 x 15
= 270 cm2

Hence, the correct answer is option (4) 270 cm2.

Monis Rasool Professor Answered on 29th December 2015.