8. The length of a rectangular picture is 4 inches longer than three times the width. If the perimeter is 56 inches, find the dimensions of the picture.

The dimensions of the picture are 8 inches and 20 inches

Step-by-step explanation:

A rectangular picture has a length 4 inches longer than three times the width, so assume that the width of the rectangle is x.

∵ The width of the rectangle = x inches

∵ Three times the width = 3 times x = 3x

∵ Four less than 3 times width = 3x - 4

∴ The length = 3x - 4 inches

Perimeter (P) of a rectangle = 2 length + 2 width, then substitute the length and the width by their values above.

∴ P = 2(x) + 2(3x - 4)

∵ P = 56 inches ⇒ given

∴ 56 = 2(x) + 2(3x - 4)

→ Simplify the right side

∵ 2(3x - 4) = 2(3x) - 2(4) = 6x - 8

∴ 56 = 2x + 6x - 8

→ Add the like terms in the right side

∴ 56 = (2x + 6x) - 8

∴ 56 = 8x - 8

→ Add 8 to both sides to move 8 from the right side to the left side

∴ 56 + 8 = 8x - 8 + 8

∴ 64 = 8x

→ Divide both sides by 8 to find x

∴

∴ 8 = x

∵ x represents the width of the picture

∴ The width of the picture is 8 inches.

∵ 3x - 4 represents the length of the picture

∴ The length = 3(8) - 4 = 24 - 4 = 20

∴ The length of the picture is 20 inches.

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step-by-step explanation: