Question

The perimeter of a rectangle is 30 inches. The length of the rectangle is twice as long as the width. What are the dimensions (length and width) of the rectangle?

Perimeter = 2L+2W
Define Variables:
Write a system and solve:
Solution sentence:

Please help me!!!

Answer 1

✫ Question -:

The perimeter of a rectangle is 30 inches. The length of the rectangle is twice as long as the width. What are the dimensions (length and width) of the rectangle?

✫ Explanation -:

Given :

• Perimeter = 30 inches
• Length is twice as long as it's width

Need to find :

• Dimensions of the rectangle rectangle

Solution :

First we will make an equation and then we will calculate the dimensions of the rectangle using the formula.

Length is twice as long as it's width

Let us assume width as x then length = 2x

We know,

`\star \: \large\boxed{ \sf{ Perimeter \: of \: a \: rectangle = 2l + 2w = 2(l + w)}}`

Where,

• L stand for Length
• B stand for Breadth

Substituting the values in the above formula

`\small\bf{ 30 = 2(2x + x)}`

`\small\rm{30 = 2(3x)}`

`\small\rm{30 = 6x}`

`\small\rm{ \cancel(30)/(6) = x}`

`\small\boxed{ \rm{x = 5}}`

Substituting the value of x = 5

Length = 2x = 2 × 5 = 10 inches

Breadth = x = 5 inches

Final Answer :

• Length = 10 inches
• Breadth = 5 inches

NOTE :

• Scroll to screen to see the solution

`\rule{90mm}{3pt}`

Answer 2

• 5 inches and 10 inches

`\\`

Explanation:

It is given that, the perimeter of a rectangle is 30 inches and the length of the rectangle is twice as long as the width and we've to find the dimensions of the rectangle.

So, Let us assume the width of the rectangle is x inches, therefore the length will be 2x inches

`\\`

Before solving it, first we have to know this formula :

`\\ {\longrightarrow \pmb{\frak {\qquad 2(Length + Width) =Perimeter_((Rectangle) )}}} \\ \\`

`{\longrightarrow \pmb{\sf {\qquad 2(2x + x) =30}}} \\ \\`

`{\longrightarrow \pmb{\sf {\qquad 4x + 2x =30}}} \\ \\`

`{\longrightarrow \pmb{\sf {\qquad 6x =30}}} \\ \\`

`{\longrightarrow \pmb{\sf {\qquad x = (30)/(6) }}} \\ \\`

`{\longrightarrow \pmb{\frak {\qquad x =5}}} \\ \\`

Therefore,

• The width of the rectangle is 5 inches .

So, we have to find the length of the rectangle :

`\\ {\longrightarrow \pmb{\frak {\qquad Length =2(x)}}} \\ \\`

`{\longrightarrow \pmb{\frak {\qquad Length =2(5)}}} \\ \\`

`{\longrightarrow \pmb{\frak {\qquad Length =10 \: inches}}} \\ \\`

Therefore,

• The dimensions of the rectangle are 5 inches and 10 inches .