Question

This picture shows a rectangle with length (3D+2)cm and width (d+5)cm.
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| |3d+2
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D+5

A) write an expression for the perimeter of the rectangle

B) given that the perimeter is 30cm, make and solve and equation for d.

C) find the area of this rectangle

Answer 1

9514 1404 393

Answer:

  A)  P = 8d +14

  B)  d = 2

  C)  56 cm^2

Step-by-step explanation:

A) The perimeter is the sum of all of the side lengths.

  P = 2(L +W)

  P = 2((3d +2) +(d +5)) = 2(4d +7)

  P = 8d +14

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B) Using 30 for P, we have ...

  30 = 8d +14

  16 = 8d . . . . . . . subtract 14

  2 = d . . . . . . . . . divide by 8

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C) The side lengths are ...

  3d +2 = 3(2) +2 = 8 . . . . cm

  d+5 = 2+5 = 7 . . . . cm

Then the area is ...

  A = LW

  A = (8 cm)(7 cm) = 56 cm^2

The area of the rectangle is 56 square centimeters.