Question

The perimeter of the rectangle below is 124 units. Find the length of side cd

Answer 1

CD = 38

Explanation:

Since AB = 3x + 2, CD = 3x + 2

To solve for the length of CD, we'll need to solve for x first by using the perimeter formula

Solving for x...

`(3x+2)+(3x+2)+2x+2x=124`

`3x + 3x + 2x + 2x = 120`

`10x=120`

`x=(120)/(10)`

`x=12`

Now that we know what x equals, plug in x into the expression of side CD

CD = 3x + 2

CD = 3(12) + 2

CD = 36 + 2

CD = 38

Therefore, the length of side CD = 38

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Check:

AB = CD | BC = DA

38 + 38 for AB and CD

BC + DA = 2x + 2x

BC + DA = 2(12) + 2(12)

BC + DA = 24 + 24

BC + DA = 48

38 + 38 + 48 = perimeter

perimeter = 124