Question

A rectangular rug has perimeter 1388 inches. The length is 34 inches more than twice the width. Find the length and width of the rug.

Answer 1

Explanation:

Comment

the perimeter formula is P = 2w + 2L

Givens

w = width. It is one of the unknowns

L = Length = 2*w + 34

Perimeter = P = 1388

Solution

1388 = 2*w + 2(2w + 34) Remove the brackets.

1388 = 2w + 4w + 68 Subtract 68 from both sides

1388 - 68 = 2w + 4w+68 - 68 Simplify

1320 = 2w + 4w Combine the right.

1320 = 6w Divide by 6

1320/6 = 6w/6

220 = w

Answer

w = 220

L = 2*220 + 34 474

Answer 2

Question - :

A rectangular rug has perimeter 1,388 inches. The length is 34 inches more than twice the width. Find the length and width of the rug.

Explanation -:

In this question we are provided with the perimeter of a rectangular rug that is 1388 inches. It is also given that the length is 34 Inches more than twice the width. We are asked to calculate the dimensions of the rug.

Let us assume width as x.

Then, length = 2x + 34

We know,

`\small\boxed{ \rm{ Perimeter_((rectangle)) = 2(length + width)}}`

Substituting the values we get

`\small\sf 1388 = 2(2x + 34 + x)`

`\small\rm{ 1388 = 2(3x + 34 )}`

`\small\rm{1388 = 6x + 68}`

`\small\rm{1388 - 68 =6x }`

`\small\rm{1320 = 6x}`

`\small\rm{ (1320)/(6) = x }`

`\small\rm{ x= 220}`

Width = 220 inches

Length = 2 × 220 + 34 = 440 + 34 = 474 inches

• Hence, the width is 220 inches and length is 474 inches