Q). The area of a right-angled triangle is 600 cm². If the base of the triangle exceeds the altitude by 10 cm, find all the three dimensions of the triangle.

(Q 33 B – 30/2/1 – CBSE 2026 Question Paper)

Ans:

Step 1: Let’s consider the Alttitude of the triangle is A

By given condition, base of the triangle exceeds the altitude by 10 cm

∴ Base = A + 10

Step 2: In a Right angled triangle, area = x Base x Altitude

= x (A + 10) x A

Since it is given that Area of triangle = 600 cm ²

∴ x (A + 10) x A = 600

∴ A (A + 10) = 1200

∴ A ² + 10 A – 1200 = 0

By mid term splitting, A ² + 40 A – 30 A – 1200 = 0

∴ A (A + 40) – 30 (A + 40) = 0

∴ (A + 40) (A – 30) = 0

∴ A = – 40 and A = 30

Step 3: Because side can not be negative, hence, we reject A = – 40

and accept A = 30 cm

∴ Altitude = 30 cm

∴  Base = A + 10 = 30 + 10

∴  Base = 40 cm

Step 4: In a right angled triangle,

Hypotenuse =

= √ 2500 = 50 cm.

Therefore, the dimensions of the triangle are 30 cm, 40 cm, 50 cm.

Check: We have altitude as 30 cm and base is 40 cm,
∴ Base exceeds the altitude by 10 cm …..it meets 1st condition
Area of triangle = (1/2) x 30 x 40 = 600 cm ²
∴ It meets 2nd condition too.
∵ both conditions are satisfied ∴ our answer is correct.

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