Question

In the figure above, PQRS is a rectangle. The area of $\Delta RST$ is $7$ and $PT=\frac{2}{5}PS$. What is the area of $\square PQRS$ ?

• A. $35$
• B. $\frac{70}{3}$
• C. $\frac{40}{3}$
  
• D. $14$

Answer 1

The correct option is B $\frac{70}{3}$

To find the area of the rectangle $PQRS$,

Let ${}^{\prime }{x}^{\prime }$ be the length of the rectangle,

$QR$ $=$ $SP$ $=$ $x$

Let ${}^{\prime }{y}^{\prime }$ be the length of the rectangle,

$PQ$ $=$ $RS$ $=$ $y$

Given

$PT$ $=$ $\frac{2}{5}$$PS$

$PT$ $=$ $\frac{2}{5}$ $\times$ $PS$

As $PS$ $=$ $x,$ $PT$ $=$ $\frac{2}{5}$ $\times$ $x$

$PT$ $=$ $\frac{2}{5}$$x$

From the figure,

$PS$ $=$ $PT$ $+$ $TS$

$x$ $=$ $\frac{2}{5}$$x$ $+$ $TS$

$TS$ $=$ $x$ $-$ $\frac{2}{5}$$x$

$TS$ $=$ $\frac{3}{5}x$

Given that

Area of $△$$RST$ $=$ $7$

$\frac{1}{2}$ $\times$ $TS$ $\times$ $RS$ $=$ $7$

$\frac{1}{2}$ $\times$ $\frac{3}{5}x$ $\times$ $y$ $=$ $7$

$xy$ $=$ $\frac{70}{3}$