Question : The two adjacent sides of a parallelogram are 12 cm and 5 cm respectively. If one of the diagonals is 13 cm long, then what is the area of the parallelogram?
Option 1: 60 cm2
Option 2: 30 cm2
Option 3: 75 cm2
Option 4: 25 cm2
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Correct Answer: 60 cm 2
Solution : In $\triangle$ABC, AB = 12 cm, BC = 5 cm and AC = 13 cm The semiperimeter ($s$) = $\frac{12+5+13}{2}$ = 15 cm So, the area of $\triangle$ABC = $\sqrt{15(15-13)(15-12)(15-5)}$ = $\sqrt{15×2×3×10}$ = 30 cm 2 Now, the area of the parallelogram ABCD = 2 × the area of $\triangle$ABC = 2 × 30 = 60 cm 2 Hence, the correct answer is 60 cm 2 .
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