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The perimeter of a rectangle is 162 cm. The length of the rectangle is eleven centimeters more than four times the width. What are the length and width of the rectangle?

Answer :

let

width = w

length = 4w + 11

2(length) + 2(width) = perimeter

2(4w + 11) + 2(w) = 162

8w + 22 + 2w = 162

10w + 22 = 162

10w = 140

w = 14 cm (WIDTH)

length = 4w + 11

length = 4(14) + 11

length = 56 + 11

LENGTH = 67 cm

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Rewritten by : Barada

The length is 4(14)+ 11 = 67 cm and width is 14 cm.

what is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Perimeter of rectangle = 162 cm

let the width be x .

then, the length is 4x+ 11

Thus, Perimeter of rectangle= 2(l + w)

162 = 2( 4x + 11 + x)

162 = 2( 5x +11)

81 = 5x+ 11

5x= 70

x= 14

Hence, the length is 4(14)+ 11 = 67 cm and width is 14 cm.

Learn more about algebra here:

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