Question

Find the area and the perimeter of a square whose diagonal is $10cm$ long.

Answer 1

Given length of the diagonal of the square is $10cm.$
$AC=10$
Let $AB=BC=x$ [Sides of square are equal in measure]
$B=90˚$ [All angles of a square are $90˚$]
$ABC$ is a right triangle.
$A{C}^2=A{B}^2+B{C}^2$
${10}^2=x^2+x^2$
$100=2x^2$
$x^2=50$
$x=\surd 50=\surd (25\times 2)$
$x=5\surd 2$
So area of square $=x^2$
$=(5\surd 2{)}^2=50c{m}^2$
Perimeter $=4x$
$=4\times 5\surd 2$
$=20\surd 2cm$
Hence area and perimeter of the square are $50c{m}^2$ and $20\surd 2cm.$