Question
One side of a right-angled triangle is twice the other, and the hypotenuse is 10 cm. The area of the triangle is :
Answer: Option A Let the sides be a cm and 2a cm
Then,
$$\eqalign{
& {a^2} + {\left( {2a} \right)^2} = {\left( {10} \right)^2} \cr
& \Rightarrow 5{a^2} = 100 \cr
& \Rightarrow {a^2} = 20 \cr} $$
∴ Area :
$$\eqalign{
& = \left( {\frac{1}{2} \times a \times 2a} \right) \cr
& = {a^2} \cr
& = 20\,c{m^2} \cr} $$
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