Question

The measures of two adjacent sides of a parallelogram are in the ratio 17:7. If the second side measures 3.5 cm, find the perimeter of the parallelogram.

Answer 1

Hint: To find the perimeter of the parallelogram, we have to first find the adjacent sides. We will denote the first side as x. The second side is given. According to the given condition, we can write the ratio as ${\displaystyle \frac{x}{3.5}}={\displaystyle \frac{17}{7}}$ . We have to solve this equation. We have to substitute the values of the adjacent sides in the formula for the perimeter of a parallelogram which is given by $P=2(a+b)$ , where a and b are adjacent sides.

Complete step by step solution:
We have to find the perimeter of the parallelogram. We are given with the measurement of second side, that is, 3.5 cm. We have to first find the first side. Let us consider the first side to be x. This is shown in the figure below.

We are also given that the two adjacent sides of a parallelogram are in the ratio 17:7.Then, according to this condition, we can write
${\displaystyle \frac{x}{3.5}}={\displaystyle \frac{17}{7}}$
Let us take 3.5 from LHS to the RHS.
$\Rightarrow x={\displaystyle \frac{17}{7}}\times 3.5$
Let us divide 3.5 by 7.
$\Rightarrow x=17\times 0.5$
On solving the above equation, we will get
$\Rightarrow x=8.5$
Now, we have two sides. Now, let us find the perimeter of the given parallelogram. We know that perimeter of a parallelogram is given by
$P=2(a+b)$
Where a and b are adjacent sides.
Therefore, perimeter of the given parallelogram is
$P=2(8.5+3.5)$
Let us add the terms inside the parenthesis.
$\begin{array}{rl}& \Rightarrow P=2\times 12\\ & \Rightarrow P=24\text{cm}\end{array}$
Hence, the perimeter of the given parallelogram is 24 cm.

Note: Students must not forget to write the unit of perimeter at the end. The perimeter of the parallelogram is similar to that of the rectangle except for the terms used. For parallelogram, we use a and b to denote the sides, while in rectangle, we use l and b that denotes the length and breadth respectively.