Answer:
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
∴ [tex]\frac{64}{8}=\frac{8x}{8}[/tex]
∴ 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.
