Question

The rectangle shown has a perimeter of 7272 cm and the given area. its length is 66 more than four timesfour times its width. write and solve a system of equations to find the dimensions of the rectangle.

Answer 1

Width = 6 Length = 30 We know the perimeter of a rectangle is simply twice the sum of it's length and width. So we have the expression: 72 = 2*(L + W) And since we also know for this rectangle that it's length is 6 more than 4 times it's width, we have this equation as well: L = 6 + 4*W So let's determine what the dimensions are. Since we have a nice equation that expresses length in terms of width, let's substitute that equation into the equation we have for the perimeter and solve. So: 72 = 2*(L + W) 72 = 2*(6 + 4*W + W) 72 = 2*(6 + 5*W) 72 = 12 + 10*W 60 = 10*W 6 = W So we now know that the width is 6. And since we have an expression telling us the length when given the width, we can easily determine the length. So: L = 6 + 4*W L = 6 + 4*6 L = 6 + 24 L = 30 And now we know the length as well.