Question

If $a$ and $b$ represents the adjacent sides of a parallelogram whose area is $15$ units, then the area of the parallelogram whose adjacent sides are $3a+2b$ and $a+3b$ is?

• A. $45$ units
• B. $75$ units
• C. $105$ units
• D. $165$ units

Answer 1

The correct option is C

$105$ units

Find the Area of parallelogram:

Given, $a$ and $b$ are two adjacent sides of a parallelogram, then

Area of parallelogram $=\mathbf{\mid }\mathit{a}\mathbf{\times }\mathit{b}\mathbf{\mid }$

$=15$

Also, sides of parallelogram are $(3a+2b)$ and$(a+3b)$

$\therefore$Area of parallelogram$\mathbf{=}\mathbf{}\mathbf{\mid }\mathbf{(}\mathbf{3}\mathit{a}\mathbf{+}\mathbf{2}\mathit{b}\mathbf{)}\mathbf{\times }\mathbf{(}\mathit{a}\mathbf{+}\mathbf{3}\mathit{b}\mathbf{)}\mathbf{\mid }$

$=\mid 7(a\times b)\mid$

$$\begin{gathered} =7\mid a\times b\mid \\ =7\times 15 \\ =\mathbf{105} \end{gathered}$$

Thus, The area of parallelogram is $\mathbf{105}$square units.

Hence, Option ‘C’ is Correct.