Question

the diagonal of a square PQRS is a+b. The perimeter of square with twice the area of PQRS is​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{The diagonal of square PQRS is a+b}$

$\underline{\textbf{To find:}}$

$\textsf{The perimeter of square with twice the area of PQRS}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Concept used:}}$

$\boxed{\mathsf{Area\;of\;square\;having\;diagonal\;d=\dfrac{1}{2}\;d^2}}$

$\implies\mathsf{Area\;of\;square\;PQRS=\dfrac{1}{2}(a+b)^2}$

$\textsf{As per given data,}$

$\textsf{Area of square with twice the area of PQRS}$

$\mathsf{=2{\times}Area\;of\;square\;PQRS}$

$\mathsf{=2{\times}\dfrac{1}{2}(a+b)^2}$

$\mathsf{=(a+b)^2}$

$\implies\textsf{Length of the side of the square= a+b}$

$\textsf{Hence, perimeter of the Square =4(a+b)}$