Question

What is the area of $△RST$ in the following figure?

• A. $84$
• B. $91$
• C. $96$
• D. $105$
• E. $120$

Answer 1

The correct option is A $84$

Given is the triangle $RST$
Let $US$ height be $x$
In triangle $RSU$, $RS=15,RU=9$
As per Pythagoras theorem, we know
hypotenuse ${}^2=$ base ${}^2+$ perpendicular ${}^2$
${15}^2=9^2+x^2$
$9^2+x^2={15}^2$
$x^2=225-81$
$x^2=144$
$x=12$
In triangle $SUT$, $ST$ is hypotenuse, $SU$ is perpendicular $UT$ is base
Let $UT$ be $y$
As per Pythagoras theorem
${13}^2={12}^2+y^2$
$y^2={13}^2-{12}^2$
$y^2=169-144$
$y^2=25$
$y=5$
Area of triangle $RST$ will be
$=\frac{1}{2}\times$ base $\times$ height .....(base will be $9+5=14$, height $=12$)
$=\frac{1}{2}\times 14\times 12=84$