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The length of a rectangle is three times of its width. If the length of the diagonal is $$8\sqrt {10} $$ cm, then the perimeter of the rectangle is :
Answer & Solution
Correct Answer:
Option
D
Let breadth = x cm
Then, length = 3x cm
$$\eqalign{ & \Rightarrow {x^2} + {\left( {3x} \right)^2} = {\left( {8\sqrt {10} } \right)^2} \cr & \Rightarrow 10{x^2} = 640 \cr & \Rightarrow {x^2} = 64 \cr & \Rightarrow x = 8 \cr} $$
So, length = 24 cm and breadth = 8 cm
∴ Perimeter = [2(24 + 8)] cm = 64 cm
Then, length = 3x cm
$$\eqalign{ & \Rightarrow {x^2} + {\left( {3x} \right)^2} = {\left( {8\sqrt {10} } \right)^2} \cr & \Rightarrow 10{x^2} = 640 \cr & \Rightarrow {x^2} = 64 \cr & \Rightarrow x = 8 \cr} $$
So, length = 24 cm and breadth = 8 cm
∴ Perimeter = [2(24 + 8)] cm = 64 cm
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