Question

A boy mows a strip 7 ft wide around a rectangular yard that he determines to be 50 percent of the yard. Find the dimensions if the width of the yard is 3/4 its length.

Answer 1

To find the dimensions of the yard, use the given information to set up equations and solve for width and length.

Step-by-step explanation:

To find the dimensions of the yard, let's denote the width of the yard as w and the length as l. According to the given information, the width of the yard is 3/4 of its length, so we can write the equation w = (3/4)l.

The boy mows a strip 7 ft wide around the yard, which is determined to be 50 percent of the yard. Therefore, the dimensions of the mowed strip will be 50 percent of the original dimensions of the yard.

Let's calculate the dimensions of the yard.

Width of the yard = w - 2(7 ft) = w - 14 ft

Length of the yard = l - 2(7 ft) = l - 14 ft

According to the question, the dimensions of the yard are 50 percent of the original dimensions, so:

w = 0.5(w - 14 ft) = (w - 14 ft)/2

l = 0.5(l - 14 ft) = (l - 14 ft)/2