In a right-angled triangle ABC such that ∠BAC = 90° and AD is perpendicular to BC. If the area of ΔABC is 63 cm², area of ΔACD = 7 cm², and AC = 5 cm, then the length of BC is equal to:

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Question

This question was previously asked in

SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 03 Jul, 2024 Shift 2)

Answer 1

Given:

Area of ΔABC = 63 cm²

Area of ΔACD = 7 cm²

AC = 5 cm

Formula used:

If ΔABC ∼ ΔXYZ, then

ar(ΔABC) / ar(ΔXYZ) = (AB/XY)² = (BC/YZ)2 = (AC/XZ)2

Calculation:

F1 SSC PriyaS 3 9 24 D6

In ΔABC and ΔACD

∠BAC = ∠ADC = 90°

∠C = ∠C (Common in both triangles)

So, ΔABC ∼ ΔDAC (by AA Similarity)

Now,

ar(ΔABC) / ar(ΔACD) = (BC/AC)²

⇒ 63/7 = (BC/5)²

⇒ 9/1 = (BC/5)2

⇒ √(9/1) = BC/5

⇒ 3 = BC/5

⇒ BC = 5 × 3 = 15 cm

∴ The length of BC is 15 cm

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