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Find the area of the largest triangle that can be inscribed in a semicircle of radius $7 cm$ .

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c m 2

c m 2

c m 2

c m 2

answer is B.

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Detailed Solution

Given that the radius of the semicircle is 7 cm.
We have to find the area of the largest triangle inscribed in the semicircle.
The area of the triangle is

A = 12 × base × altitude

.
Consider the figure,

Area of the largest triangle that can be inscribed in a semi ...

Here,

∠ A C B = 90 °

. So,

Area of Δ ABC = Area of Δ ADC + Area of Δ DBC ⇒ Area of Δ ABC = 12 × A D × C D + 12 × B D × C D ⇒ Area of Δ ABC = 12 × 7 × 7 + 12 × 7 × 7 ⇒ Area of Δ ABC = 492 + 492

⇒ Area of Δ ABC = 49

Thus, Area of

Δ A B C = 49 c m 2

.
The area of the largest triangle that can be inscribed in a semicircle of radius 7 cm is

49 c m 2 .

Therefore, the correct option is 2.

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