Question

The area of a trapezium is $385{cm}^2.$ Its parallel sides are in the ratio $3:4$ and the perpendicular distance between them is $11cm.$ Its longer side is

• A. $35cm$
• B. $30cm$
• C. $40cm$
• D. $60cm$

Answer 1

The correct option is A $35cm$

$\begin{array}{c}\text{Solution - let length of}11\text{sides of traperium}\\ \text{be}a\text{and}b\\ \begin{array}{c}\text{ATQ}:\frac{a}{b}=\frac{3}{4}\Rightarrow a=\frac{3}{4}b\\ \text{height}=11cm\\ \text{Area}=385{cm}^2\\ \text{Arua}=\frac{1}{2}\times [a+b]\times h\\ 384=\frac{1}{2}[\frac{3b}{4}+b]\times 11\\ \frac{384\times 2}{11}=\frac{7b}{4}\Rightarrow b=35cm\end{array}\\ \text{Hence,}\left(A\right)\text{is the correct option.}\end{array}$