Final answer:
To find the dimensions of Kent's rectangular decor with an area of 1500 square inches and a width one-twelfth of the length, we solve for the length (L) using the equation L * (L/12) = 1500, then calculate the width (W) by dividing the length by 12. The approximate dimensions are 134.16 inches for the length and 11.18 inches for the width.
Step-by-step explanation:
Let's represent the length of the rectangular decor by L, and since the width is one-twelfth of the length, the width will be W = L/12. We're given that the area of the decor is 1500 square inches, and the area of a rectangle is calculated by multiplying its length and width, so we have the equation: L * (L/12) = 1500.
To find the dimensions of the decor, we start by solving for L. Multiplying both sides of the equation by 12 gives us L^2 = 18000. Taking the square root of both sides reveals that L = 134.16 (rounded to two decimal places), which is the length in inches. We can now determine the width by dividing the length by 12, yielding W = 11.18 inches (rounded to two decimal places).
Therefore, the dimensions of Kent’s rectangular decor are approximately 134.16 inches in length and 11.18 inches in width.