Q).  The length of hypotenuse (in cm) of a right-angled triangle is 6 cm more than twice the length of its shortest side. If the length of its third side is 6 cm less than thrice the length of its shortest side, find the dimensions of the triangle.

(Q 35 B – 30/2/3 – CBSE 2026 Question Paper)

Ans:

Step 1: Let’s consider, length of its shortest side = X cm

By 1st condition, “hypotenuse is 6 cm more than twice the length of its shortest side”.

∴ length of hypotenuse = 2 X + 6

Step 2: Now by 2nd condition, “length of its third side is 6 cm less than thrice the length of its shortest side”

∴ length of third side = 3 X – 6

Step 3: By Pythagoras theorem, (Hypotenuse) ² = (Shortest side) ²+ (Third side) ²

∴ (2 X + 6) ² = (X) ² + (3 X – 6) ²

∴ 4 X ² + 36 + 24 X = X ² + (9 X ² + 36 – 36 X)

∴ 4 X ² + 36 + 24 X = 10 X ² + 36 – 36 X

∴ 4 X ² + 24 X = 10 X ² – 36 X

∴ 10 X ² – 36 X – (4 X ² + 24 X) = 0

∴ 10 X ² – 36 X – 4 X ² – 24 X = 0

∴ 6 X ² – 60 X = 0

∴ X ² – 10 X = 0

∴ X (X – 10) = 0

∴ X = 0 and X = 10

Step 4: Here, we reject X = 0, because length of a side in a triangle can not be 0.

We accept, X = 10,

∴ length of shortest side = 10 cm

∴ length of hypotenuse = 2 X + 6 = 2 (10) + 6 = 26 cm

∴ length of third side = 3 X – 6 = 3 (10) – 6 = 24 cm

Therefore, dimensions of the three sides of the right-angled triangle are 10 cm, 26 cm and 24 cm.

Check: If sides of a right-angled triangle are 10, 24, 26
then it should satisfy Pythagoras theorem
∴ (10) ² + (24) ² = (26) ²
∴ 100 + 576 = 676
Since the above equation is balanced, our answer is correct.

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