Question

Find the area and perimeter of a square plot of land, the length of whose diagonal is $15$ metres. Give your answer correct to $2$ places of decimals.

• A. $110.50$ sq. m and $40.43$ m
• B. $115.50$ sq. m and $45.43$ m
• C. $112.50$ sq. m and $42.43$ m
• D. $113.50$ sq. m and $43.43$ m

Answer 1

Answer: (C)

$112.50$ sq. m and $42.43$ m

Let the side of the square be $x$
Thus, ${15}^2=x^2+x^2$
$\Rightarrow 225=2x^2$
$\Rightarrow x^2=112.5$
$\Rightarrow x=10.61$
Thus, area of the square $=112.5$ sq. m
Perimeter $=4x$
$=4\times 10.61$
$=42.43$ m