Question
Find the perimeter of the rectangle whose length is 40cm and a diagonal is 41cm.
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Answer
Given,
$A B C D$ is a rectangle and $A C$ is its diagonal.
$AB =40 cm$ and $AC =41 cm$
Now in right $\triangle ABC$,
$A C^2=A B^2+B C^2(B y \text { Pythagoras Theorom) } \\
\Rightarrow(41)^2=(40)^2+B C^2 \\
\Rightarrow 1681=1600+B C^2 \\
\Rightarrow B C^2=1681-1600 \\
\Rightarrow B C^2=81 \\
\Rightarrow B C^2=(9)^2 \\
B C=9 cm$
Now perimeter of rectangle $A B C D=2(A B+B C)=2(40+9)=2 \times 49=98 cm$.
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