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1. The perimeter of an isosceles triangle is equal to 14 cm and the lateral side is to the base in the ratio 5 : 4. The area of the triangle is :

A. 21 cm²

B. $0.5 \sqrt{21}$ cm²

C. $1.5 \sqrt{21}$ cm²

D. $2 \sqrt{21}$ cm²

Solution:

Let the sides of the triangle be 5x, 5x and 4x cm respectively
Then,
5x + 5x = 4x + 14
⇒ 14 x = 14
⇒ x = 1
So, a = 5 cm, b = 5 cm, c = 4 cm

\begin{aligned} s = \frac{a  +  b  +  c}{2} \\ = (\frac{14}{2}) c m \\ = 7 c m \end{aligned}

(s - a) = 2 cm, (s - b) = 2 cm, (s - c) = 3 cm
∴ Area of the triangle :

\begin{aligned} = \sqrt{7 \times 2 \times 2 \times 3} \\ = 2 \sqrt{21} c m^{2} \end{aligned}

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