question_answer

The area of a quadrilateral is 342 sq. m. The perpendiculars from two of its opposite vertices to the diagonal are 12 m and 12 m. What is the length of the diagonal?

A)  28.6cm          

B)         25.3cm          

C)  28.5cm          

D)         22.5cm          

Correct Answer: C

Solution :

Let ABCD be a quadrilateral. DE, BF are perpendiculars drawn to AC. We have DE= BF= 12 m Area of quadrilateral ABCD = Area of \[(\Delta ACD+\Delta ABC)\] \[\Rightarrow 342=\frac{1}{2}\times AC\times BF+\frac{1}{2}\times AC\times DE\] \[\Rightarrow 342=\frac{1}{2}\times AC(BF+DE)=\frac{1}{2}\times AC\times 24\] \[\Rightarrow AC=\frac{2\times 342}{24}=28.5cm\]