Math

QuestionFind the area of a rectangle where the length is 22 inches less than 22 times the width and the perimeter is 7474 inches.

Studdy Solution

STEP 1

Assumptions1. The length of the rectangle is inches less than twice its width. . The perimeter of the rectangle is74 inches.
3. The formula for the perimeter of a rectangle is (length+width)*(length + width).
4. The formula for the area of a rectangle is lengthwidthlength * width.

STEP 2

Let's denote the width of the rectangle as ww. According to the problem, the length of the rectangle is2 inches less than twice its width, so we can express the length as 2w22w -2.

STEP 3

Now we can write the equation for the perimeter of the rectangle using the given perimeter and the expressions for the length and width.
2(length+width)=742*(length + width) =74

STEP 4

Substitute the expressions for the length and width into the equation.
2((2w2)+w)=742*((2w -2) + w) =74

STEP 5

implify the equation.
2(3w2)=742*(3w -2) =74

STEP 6

Expand the equation.
6w4=746w -4 =74

STEP 7

Add4 to both sides of the equation to isolate the term with ww.
6w=786w =78

STEP 8

Divide both sides of the equation by6 to solve for ww.
w=78/6w =78 /6

STEP 9

Calculate the value of ww.
w=13w =13

STEP 10

Now that we have the width, we can find the length by substituting ww into the expression for the length.
length=2w2length =2w -2

STEP 11

Substitute w=13w =13 into the equation.
length=13length =*13 -

STEP 12

Calculate the length.
length=24length =24

STEP 13

Now that we have both the length and the width, we can calculate the area of the rectangle using the formula for the area of a rectangle.
Area=lengthwidthArea = length * width

STEP 14

Substitute the values for the length and width into the equation.
Area=2413Area =24 *13

STEP 15

Calculate the area.
Area=312Area =312The area of the rectangle is312 square inches.

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