Question

The length of a rectangle is 3 times its width. The perimeter of the rectangle is 48m.
What are the dimensions of the rectangle? Also find its area. want more than 1 people please .

Answer 1

Answer:

Length = 18m, Width = 6m, Area = 108m²

Step-by-step explanation:

Let,

Width = x    , Length = 3x

Perimeter of a rectangle = 2(length + width)  

= 48m = 2(x + 3x)

= 2(x + 3x) = 48m

= 2 × 4x = 48m

= 4x = 48/2

= 4x = 24

= x = 24/4 = 6

∴ x = 6

therefore,

Width = x = 6m

Length = 3x = (3 × 6)m  = 18m

Also,

Area of a rectangle = LENGTH × WIDTH

                                  =(6×18)m² = 108m²

∴ Area = 108²

Hope it helps :)

Answer 2

Given : The length of a rectangle is 3 times its width and the perimeter of the rectangle is 48m.

Need To Find : Area and Dimensions [ Length and width ] of Rectangle.

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$\sf{\bf{ Solution \:of\;Question \::}}$ Let's consider the Width of Rectangle be x m .

Given that ,

⠀⠀⠀⠀⠀ The length of a rectangle is 3 times its width .

⠀⠀⠀⠀

⠀⠀⠀⠀⠀" Width = x m"

Then ,

⠀⠀⠀⠀⠀Length of Rectangular is 3x m

⠀⠀⠀⠀⠀ We know that if we are given with value of Perimeter and we have already assumed the value of Width and with the help of Width and According to question we have dind the Length . And now we need to find the exact measure of Dimensions [ Length and Width ] by using the formula that is :

⠀⠀⠀⠀⠀$\implies {\underline{\sf{\pink{ Perimeter _{( Rectangle)} = 2 ( l + w )\:\:units }}}}$

⠀⠀⠀⠀⠀Here l is the length of Rectangle & w is width of Rectangle and we have given with the value of Perimeter and we have already assumed the values of Length and Width . And Perimeter = 48 m , Length (l) = x m & Width (w) = 3x m . So by using the given and Assumed value we can find the value of 'x' :

⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀$\underline {\sf{\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}}$

⠀⠀⠀⠀

⠀⠀⠀⠀⠀$\longmapsto {\sf{ 48\:m = 2 ( x + 3x ) }}$

⠀⠀⠀⠀⠀⠀⠀$\longmapsto {\sf{ 48 \: m = 2 ( 4x ) }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀$\longmapsto {\sf{ \dfrac{\cancel {48}}{\cancel{2}} \: = 4x }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\longmapsto {\sf{ 24 \: = 4x }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\longmapsto {\sf{x = \dfrac{\cancel {24}}{\cancel{4}} \: }}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm { x = 6 \: m}}}}$

Therefore,

• Length of Rectangle = x = 6 m.

• Breadth of Rectangle = 3x = 3 × 6 = 18 m

Therefore,

⠀⠀⠀⠀⠀$\underline {\therefore\:{\pink{ \mathrm { Hence,\:The\:Dimensions \: ( Length \:and\:Width)\:of\:Rectangle \:is\: 6m\:and\:18m\:,respectively. }}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀⠀⠀⠀As we have found the exact measure of Length and Width of Rectangle and now we have to find the Area of Rectangle using Length and Width of Rectangle and we need one formula that is :

⠀⠀⠀⠀⠀$\implies {\underline{\sf{\pink{ Area _{( Rectangle)} = l \times w \:\:sq.units }}}}$

⠀⠀⠀⠀⠀Here l is the length of Rectangle & w is width of Rectangle and we have found the value of Length and width of Rectangle. And Length (l) = 6 m & Width (w) = 18 m . So by using this given Values and formula for Area of Rectangle we can Find the Area of Rectangle:

⠀⠀⠀⠀⠀⠀$\underline {\sf{\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}}$

⠀⠀⠀⠀⠀$\longmapsto {\sf{ Area _{( Rectangle)} = 6 \times 18 }}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm { Area_ {(Rectangle)} = 108 \: m^{2}}}}}$

Therefore,

⠀⠀⠀⠀⠀$\underline {\therefore\:{\pink{ \mathrm { Hence,\:The\:Area \: \:of\:Rectangle \:is\: 108m^{2}\:\:. }}}}$

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$\Large{\boxed{\bf{\mathrm |\:\:{\underline {More \:To\;know\::}}\:\:|}}}$

⠀⠀⠀⠀⠀Some Formulas of Areas of Shapes :

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• Area of Rectangle = Length × Breadth sq. units

• Area of Square = Side² sq.units

• Area of Triangle = ½ × Base × Height sq.units

• Area of Parallelogram = Base × Height sq.units

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