Question

A string of length $12$ is bent first into a square PQRS and then into an isosceles triangle PQT by keeping the side PQ of the square as base then area of the Square PQRS: area of the triangle PQT$=?$

Answer 1

Side $PQ$ of the square $PQRS=\frac{12}{4}=3$

Hence, side $PT$ and $QT$ = $\frac{9}{2}=4.5$

Height = ${4.5}^2-{1.5}^2=h^2$

$h=\sqrt{18}$

area of triangle = $\frac{\sqrt{18}\times 4.5}{2}$

area of square = $9$

Ratio = $\frac{\sqrt{18}}{4.5}$

$\frac{2}{\sqrt{4.5}}$