Question : $P Q R S$ is a rectangle. $T$ is a point on $P Q$ such that $R T Q$ is an isosceles triangle and $P T=5 \mathrm{QT}$. If the area of triangle RTQ is $12 \sqrt{3}$ sq.cm, then the area of the rectangle PQRS is:
Option 1: $144 \sqrt{3}$ sq.cm
Option 2: $142$ sq. cm
Option 3: $134 \sqrt{3}$ sq. cm
Option 4: $142\sqrt{3}$ sq. cm

Question

Question : $P Q R S$ is a rectangle. $T$ is a point on $P Q$ such that $R T Q$ is an isosceles triangle and $P T=5 \mathrm{QT}$. If the area of triangle RTQ is $12 \sqrt{3}$ sq.cm, then the area of the rectangle PQRS is:

Option 1: $144 \sqrt{3}$ sq.cm

Option 2: $142$ sq. cm

Option 3: $134 \sqrt{3}$ sq. cm

Option 4: $142\sqrt{3}$ sq. cm

Team Careers360 · Accepted Answer

Correct Answer: $144 \sqrt{3}$ sq.cm

Solution :
Given: $PT = 5QT$
$PT : QT = 5 : 1$
Let the ratio of $PT : QT$ be $5x : x$.
⇒ $PQ = PT + QT$
⇒ $PQ = 5x + x$
⇒ $PQ = 6x$
Area of $ riangle RTQ = \frac{1}{2} imes base imes height$
⇒ $\frac{1}{2} imes x imes RQ = 12\sqrt3$
⇒ $x imes RQ = 24\sqrt3 $
Area of rectangle PQRS = $PQ imes RQ$
= $6x imes RQ$
= $6 imes 24\sqrt3 $
= $144\sqrt3 $
Hence, the correct answer is $144\sqrt3$ sq. cm

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Question : PQRS is a rectangle. T is a point on PQ such that RTQ is an isosceles triangle and PT=5QT. If the area of triangle RTQ is 123 sq.cm, then the area of the rectangle PQRS is:Option 1: 1443 sq.cmOption 2: 142 sq. cmOption 3: 1343 sq. cmOption 4: 1423 sq. cm

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