Mr reed is drawing a blueprint of a rectangular patio. the width of the patio is 40.75 feet shorter than twice it's length. the perimeter of the patio is 86.5 feet. what is the length of the patio?

The length of the given rectangular patio: L = 28 feet

Step-by-step explanation:

Rectangle is a two-dimensional shape having 4 sides and 4 vertices. It has equal angles and equal alternate sides. Also all the sides of a rectangle are perpendicular to each other.

If a given rectangle has width (W) and length (L), then

The perimeter of the rectangle = 2W + 2L = 2[W + L]

Given: For the rectangular patio, W = 2L - 40.75 feet

Perimeter of rectangular patio = 86.5 feet

L = ? feet

As, Perimeter = 2[W + L]

⇒ 86.5 feet = 2 [(2L - 40.75 feet) + L] = 2 [(3L - 40.75 feet]

⇒ 86.5 feet = 6L - 81.5 feet

⇒ 6L = 86.5 + 81.5 = 168 feet

⇒ L = 168 ÷ 6 = 28 feet

∴ The length of the given rectangular patio: L = 28 feet