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
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 $\triangle RTQ = \frac{1}{2} \times base \times height$ ⇒ $\frac{1}{2}\times x \times RQ = 12\sqrt3$ ⇒ $x \times RQ = 24\sqrt3 $ Area of rectangle PQRS = $PQ \times RQ$ = $6x \times RQ$ = $6 \times 24\sqrt3 $ = $144\sqrt3 $ Hence, the correct answer is $144\sqrt3$ sq. cm
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : Find the area of triangle whose sides are 10 cm, 12 cm, and 18 cm.
Question : The area of an equilateral triangle is $4 \sqrt{3} \mathrm{~cm}^2$. Find the side (in cm) of the triangle.
Question : Find the area of a triangle whose length of two sides are 4 cm and 5 cm and the angle between them is 45°.
Question : One side of the triangle is 15 cm and the corresponding height is 6 cm, then area of the triangle is:
Question : In a triangle ABC, if $\angle B=90^{\circ}, \angle C=45^{\circ}$ and AC = 4 cm, then the value of BC is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile