Question

Figure PQRS represents the top view of a rectangular room. Find its area.

• A. 135 sq in
• B. 120 sq in
• C. 90 sq in
• D. 145 sq in

Answer 1

The correct option is B 120 sq in

We know,
Area of a rectangular room = Length x Breadth

Given: Breadth = 8 ft

Apply pythgoras theorem in triangle PQR to find the length of the rectangle,

$P{Q}^2+Q{R}^2=P{R}^2$ (By pythagoras theorem)
where,
QR = 8 ft
PR = 17 ft

$\left(P{Q}^2\right)+\left(8^2\right)=\left({17}^2\right)$

$\left(P{Q}^2\right)=\left({17}^2\right)-\left(8^2\right)$

$\left(P{Q}^2\right)=\left(289\right)-\left(64\right)$

$\left(P{Q}^2\right)=225$

⇒ Length (PQ) = <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> 15 ft

$\text{Area of PQRS =}15\times 8$
$=120\text{sq. in}$