Question

If the perimeter of the rectangle having sides in a ratio is 3:2 is 80 cm then find the length of the rectangle​

Answer 1

Step-by-step explanation:

$\large{ \underline {\underline { \bf{ \orange{Given \: information : - - - }}}}}$

• Perimeter of rectangle is 80vm
• Rectangle having sides in ratio is 3:2

$\large{ \underline {\underline { \bf{ \orange{ What \;we \: have \: to \: calculate: - - - }}}}}$

• We have to calculate length of the rectangle?

$\large{ \underline {\underline { \bf{ \green{ How \;we \: solve \: this \: type \: of \: question : - - - }}}}}$

• Assume a variable ( unknown) .For example = x .
• According to the given question, setup the two equation in terms of x

$\large{ \underline {\underline { \bf{ \orange{ Let \;assume \;: - - - }}}}}$

• length of the rectangle be x

$\large{ \underline {\underline { \bf{ \blue{ Finding \; length \: of \;rectangle: - - - }}}}}$

• To find length of rectangle . We have to multiply both ratio by x we get

Length ratio

⇒ 3× x

⇒ 3x

Breadth ratio

⇒2 × x

⇒2x

Therefore length and breadth of the rectangle are 3x and 2x.

$\bf \large \underline{ \underline{ \red{Formula \: using : - - - }}}$

$\longrightarrow \underline{ \boxed{ \sf \: \red{Perimeter _{(rectangle)} 2(l+b)}}}$

were,

• l = length
• b = breadth

$\bf \large \underline{ \underline{ \pink{Diagram \: of \: rectangle : - - - }}}$

$\\ \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} {\begin{gathered} \sf{ 16\:cm} \: \: \: \huge\boxed{ \begin{array}{cc} \: \: \: \: \: \\ \: \: \: \: \: \: \: \: \: \qquad \end{array}} \\ \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \: 24cm} \end{gathered}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\bf \large \underline{ \underline{Solving : - - - }}$

As given that perimeter of the rectangle is 80 centimeter .now solving by applying formula of perimeter

$\\ \\ \sf: \longmapsto \red{Perimeter \: of r \: ectangle = 2(length × breadth)} \\ \\ \\ \pmb{ \underline{putting \: value}} \\ \\ \\ \bf: \longmapsto80 =2(3x + 5x)$

• Adding 3x & 2x We get = 5x

$\\ \bf: \longmapsto80 =2 \times 5x$

• transferring 2 and diving 80 by 2

$\\ \bf: \longmapsto \frac{ \cancel{80}}{ \cancel2} = 5x$

• we get 40

$\\ \bf: \longmapsto40 =5x$

• Again transfer 5 and Dividing by 40 by 5

$\\ \bf: \longmapsto \: x = \frac{ \cancel{40}}{ \cancel5}$

• now we get the value of x

$\\ \\ \bf: \longmapsto \underline{ \boxed{ \frak{x = 8}}}$

$\rule{80mm}{1mm}$

$\large \bf \underline {\underline{Finding \: out \: length : - - - }}$

Again give

• length & breadth of rectangle is 3x and 2x
• and value of x is 8

Substituting values of x we get

• ⇒3x
• ⇒3(8)
• ⇒24cm

now solving for breadth

• ⇒2x
• ⇒2(8)
• ⇒16cm

$\maltese \: \: \underline{ \textbf{ \textsf{Therefore length of the rectangle is 24cm}}}$

Answer 2

Answer:

Hence, value of length and breadth of the rectangle will be

$Length = 3x = (3\times 8) = 24\:cm\\Breadth = 2x (2 \times 8) = 16\:cm$

Step-by-step explanation:

In context to the question asked,

We have to determine the value of length and breadth of the rectangle.

As per data given in the question,

It is given that,

Side of rectangle are in ratio of 3 : 2

Perimeter of rectangle = 80 cm

As we know that,

Perimeter of rectangle can be determined by using the formula $Perimeter = 2 (l +b)$

So, let the length and breadth of rectangle are 3x and 2x respectively.

So, in order to determine the value of length and breadth we will put the assumed value of length and breadth of rectangle in above formula.

Thus we will get,

$Perimeter = 2 (3x+2x)\\=>80= 2 \times 5x\\=>10x = 80\\=>x = \frac{80}{10} = 8$

So, value of length and breadth of the rectangle will be

$Length = 3x = (3\times 8) = 24\:cm\\Breadth = 2x (2 \times 8) = 16\:cm$