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1. In ΔPQR, side PQ = 3 cm and side PR = 25 cm. What is the area of ΔPQR ?

A. $2 \sqrt{154} sq .cm$

B. $3 \sqrt{154} sq .cm$

C. $4 \sqrt{308} sq .cm$

D. Cannot be determined

Solution:

\begin{aligned} Area of Δ P Q R \\ = \frac{1}{2} \times Q R \times P Q \\ Given, P Q = 3 c m \\ Q R = \sqrt{{(P R)}^{2} - {(P Q)}^{2}} \\ = \sqrt{{(25)}^{2} - 3^{2}} c m \\ = \sqrt{625 - 9} c m \\ = \sqrt{616} c m \\ = 2 \sqrt{154} c m \\ ∴ Area of Δ P Q R \\ = (\frac{1}{2} \times 2 \sqrt{154} \times 3) c m^{2} \\ = 3 \sqrt{154} c m^{2} \end{aligned}

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