Question

Let $PQRS$ be a rectangle such that $M$ and $N$ are points on $RS$ and $QR$ and are of $△PMS,△MRN,$ and $△PQN$ are $32{cm}^2$, $18{cm}^2$ and $50{cm}^2$ respectievely. Find the area of $△PMN$

• A. $40{cm}^2$
• B. $72{cm}^2$
• C. $96{cm}^2$
• D. $60{cm}^2$

Answer 1

The correct option is D $60{cm}^2$

R.E.F.Image.

$(x-\frac{64}{y})(y-\frac{100}{x})=36$

$(xy-64)(xy-100)=36xy$

$(xy{)}^2-164xy+6400=36xy$

$(xy{)}^2-200xy+6400=0$

$(xy-160)(xy-40)=0$

xy = Area of the rectangle

$\therefore$ xy cannot be 40.

so, xy = 160

area of $\Delta PMN=160-(32+18+50)$

$=160-100$

$=60c{m}^2$