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The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.

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12 and 24 cm

5 and 10 cm

15 and 20 cm

5 and 7 cm

answer is C.

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Detailed Solution

Given:
The hypotenuse of a right triangle is 25 cm, and the difference between the lengths of the other two sides of the triangle is 5 cm.
Consider

△ A B C

be a required right-angle triangle with

∠ B = 90 °

Consider the length of one side of a triangle is x cm.
Since, the difference between the lengths of the other two sides is 5 cm.
It means that the other side must be 5 cm greater than the first side.
Hence, the length of the other side is

(x + 5) cm

Apply Pythagoras theorem,

⇒ (A B) 2 + (B C) 2 = (A C) 2 ⇒ x 2 + (x + 5) 2 = 252 ⇒ x 2 + x 2 + 10 x + 25 = 625 ⇒ 2 x 2 + 10 x + 25 − 625 = 0 ⇒ 2 x 2 + 10 x − 600 = 0

Divide both sides by 2

x 2 + 5 x − 300 = 0

⇒ x 2 + 20 x − 15 x − 300 = 0 ⇒ x (x + 20) − 15 (x + 20) = 0 ⇒ (x − 15) (x + 20) = 0

⇒ x − 15 = 0 or x + 20 = 0 ⇒ x = 15, − 20

But,

x = − 20

is not possible as length can’t be negative.
Therefore,

x = 15

Since, length of one side of the triangle is x cm.
The length of the other side,

⇒ (x + 5) cm ⇒ (15 + 5) cm ⇒ 20 cm

Therefore, the lengths of sides of the triangle are 15 cm and 20cm.
So, the correct option is 3.

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