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In ΔABC, ∠A = 90° and radius of the in-circle of the ΔABC is 3 cm and BC = 17 cm, then, what is the area (in sq. cm) of the ΔABC?

In ΔABC, ∠A = 90° and radius of the in-circle of the ΔABC is 3 cm and BC = 17 cm, then, what is the area (in sq. cm) of the ΔABC? Correct Answer 60

Given:

∠A = 90°

Radius of the in-circle of the ΔABC = 3 cm

 BC = 17 cm

Formula used:

Area of ΔABC = semi perimeter × radius

Calculation:

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In ΔABC, ∠A = 90° and BC = (BD + EC) = 17 cm

Now, the perimeter of ΔABC = AB + BC + CA = (AD + DB) + BC + (CE + AE)

⇒ AD + (BD + EC) + BC + AE

We know that AE = AD = radius of incentre

⇒ 3 + (17) + 17 + 3

⇒ 40 cm

So, the semi-perimeter (s) of ΔABC = 40/2 = 20 cm

Area of ΔABC = s × r

⇒ Area of ΔABC = 20 × 3 = 60 sq. cm

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