In △ ABC, ∠ C = 90°; D is the midpoint of BC; and DE ⊥ AB at E. IF AB = 13 cm and BE = 5 cm, then the area of the square drawn on BC is equal to:

In △ ABC, ∠ C = 90°; D is the midpoint of BC; and DE ⊥ AB…

In $\triangle$ ABC, $\angle$ C = 90°; D is the midpoint of BC; and DE $\perp$ AB at E. IF AB = 13 cm and BE = 5 cm, then the area of the square drawn on BC is equal to:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1 i.e. 130 cm².

AE = 13 - 5 = 8 cm

Let BC = x cm, AC = y cm

x² + y² = 13² = 169 .....(1)

Since DE ⊥ AB and ∠B are common, ΔABC ~ ΔDBE.

BD/AB = BE/BC ⇒ (x/2)/13 = 5/x

⇒ x = √130

Area of the square on BC = (√130)² = 130 cm²

SSC Selection Post 2020 PYQ — Question 69