# 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

- 450 sq. cm
- 540 sq. cm
- 180 sq. cm
- 270 sq. cm

**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, X^{2} + (X – 21)^{2} = 39^{2}

X^{2} + X^{2} + 21^{2} – 2 x 21 X = 39 x 39

2 X^{2} + 441 – 42 X = 1521

2 X^{2} + 441 – 42 X – 1521 = 0

2 X^{2} – 42 X – 1080 = 0

2 X^{2} – 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 cm^{2}

Hence, the correct answer is option (4) 270 cm^{2}.