Question

The perimeter of a parallelogram is 42 cm. The smaller side is 8cm long. Then the length of the longer side is

Answer 1

Answer

• The length of the longer side = 13 cm.

Given

• The perimeter of a parallelogram = 42 cm.
• Length of the smaller side = 8 cm.

To Find

• The length of the longer side.

Step By Step Explanation

We know that,

In a parallelogram opposite sides and angles are equal and parallel.

Assumption :

Let us assume the length of the longer side be x.

Equation :

$\red\bigstar{ \underline{ \boxed{ \bold{8 + 8 + x + x = 42}}}}$

Solution of Equation :

Let us solve the above equation to find the length of the longer side.

$\longmapsto \sf42 = 8 + 8 + x + x \\ \\\longmapsto \sf 42 = 16 + 2x \\ \\ \longmapsto \sf42 - 16 = 2x \\ \\\longmapsto \sf 26 = 2x \\ \\\longmapsto \sf \cancel\cfrac{26}{ 2} = x \\ \\\longmapsto{ \underline{\boxed{ \bold{\green{13 = x}}}}} \: \: \bigstar$

Therefore, the length of longer side = 13 cm.

__________________________

Answer 2

$\begin{gathered}{\textsf{\textbf{\underline{\underline{Solution :}}}}}\end{gathered}$

$\begin{gathered}\begin{gathered}\mapsto\rm the \: perimeter \: of \: a \: parallelogram = 42\rm \end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\mapsto\rm\ the \: smaller \: side \: of \: a \: parallelogram = 8cm \rm \end{gathered} \end{gathered}$

$\begin{gathered}{\textsf{\textbf{\underline{\underline{To find :}}}}}\end{gathered}$

$\begin{gathered}\begin{gathered}\mapsto\rm\ \ the \: longer \: side \:of \: a \: parallelogram \: \rm \end{gathered} \end{gathered}$

$\begin{gathered}{\textsf{\textbf{\underline{\underline{we know that:}}}}}\end{gathered}$

$\red \bigstar\begin{gathered}\begin{gathered}\rm\ in \: a \: parallelogram \: opposite \: sides \: are \: equal.\rm \end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\rm\ let \: the \: length \: of \: longer \: side \: be \: x.\rm \end{gathered} \end{gathered}$

$\purple{\begin{gathered}\begin{gathered}\rm\ perimeter = x + x + 8 + 8 = 42cm.\rm \end{gathered} \end{gathered} }$

$\begin{gathered}{\textsf{\textbf{\underline{\underline{now \: solve \: the \: equation:}}}}}\end{gathered}$

$\implies \bold{8 + 8 + x+ x = 42}$

$\implies \bold{16+ 2x = 42}$

We will shift the 2x to the left and 16 to the right.

$\implies \bold{ 2x= 42 - 16}$

$\implies \bold{2 x = 26}$

$\implies \bold{ x = \cancel\frac{26}{2} }$

$\pink\implies \bold{ x = 13}$

Therefore, the required answer is 13cm.