Question 107
A parallelogram has sides 60 m and 40m and one of its diagonals is 80 m long. Its area is
Solution
Area of a triangle=$$\sqrt{s(s-a)(s-b)(s-c)}$$ (Heron's Formula)
In $$\triangle$$ABC,
a=60,b=40,c=80
s=$$\frac{a+b+c}{2}=\frac{40+60+80}{2}$$
$$s=90$$
Area of $$\triangle$$ABC=$$\sqrt{90(90-60)(90-40)(90-80)}$$
$$=\sqrt{90\times30\times50\times10}$$
$$=300\sqrt{15}$$
Area of parallelogram ABCD=$$2\times$$ Area of $$\triangle$$ABC
$$=2\times300\sqrt{15}$$
$$=600\sqrt{15}$$
Hence, Option B is correct.
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