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One side of a right-angled triangle is twice the other, and the hypotenuse is 10 cm. The area of the triangle is :
Answer & Solution
Correct 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 :
$$\eqalign{ & = \left( {\frac{1}{2} \times a \times 2a} \right) \cr & = {a^2} \cr & = 20\,c{m^2} \cr} $$
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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