Question

If the area of the parallelogram with $a$ and $b$ as two adjacent sides is $15$ sq units, then the area of the parallelogram having, $3a+2b$ and $a+3b$ as two adjacent sides is sq unit is

• A. $120$
• B. $105$
• C. $75$
• D. $45$

Answer 1

The correct option is B $105$

We know, if $a$ and $b$ are two adjacent sides of a parallelogram, then
Area $=|a\times b|=15$ (given) ...(i)
If the sides are $(3a+2b)$ and $(a+3b)$
Area of parallelogram $=|(3a+2b)\times (a+3b)|$
$=\left|7(a\times b)\right|$
$=7|a\times b|$
$=7\times 15$ ....[from equation (i)]
$=105$ sq units