In a right-angled triangle, the hypotenuse is 2 cm longer than the perpendicular which is 2 cm longer than the base. Calculate the length of the base. A) 6 cm B) 9 cm C) 10 cm D) 8 cm?

C
B
A
D

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 3 : A

Let, length of the base = x cm

Length of perpendicular = (x + 2) cm

Length of hypotenuse = (x + 4) cm

According to the questions,

⇒ x² + (x + 2)² = (x + 4)²

⇒ x² + x² + 4x + 4 = x² + 8x + 16

⇒ x² – 4x – 12 = 0

⇒ x² – 6x + 2x – 12 = 0

⇒ x(x – 6) + 2(x – 6) = 0

⇒ (x – 6) (x + 2) = 0

⇒ x = 6 or – 2

∴ Length of the base = 6 cm

4 views Answered 2022-09-04 04:29

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