Question

Find the perimeter of the rectangle whose length is $40cm$ and a diagonal is $41cm.$

Answer 1

Given: Length of rectangle, $AB=40cm$
Diagonal, $AC=41cm$
Then, by Pythagoras theorem in right △ABC:
$A{C}^2=A{B}^2+B{C}^2$

$\Rightarrow B{C}^2={41}^2-{40}^2$

$\Rightarrow B{C}^2=1681-1600$

$\Rightarrow B{C}^2=81$

$\Rightarrow B{C}^2=9^2$

$\Rightarrow BC=9cm$
∴ Length $=40cm$ and Breadth $=9cm$
∴ Perimeter of the rectangle $=2$(length $+$ breadth) $=2(40+9)=98cm$