CSC and BLEPT Math Review Problem 2

Math Problem 2

A rectangular garden has a length that is 4 meters longer than its width. The perimeter of the garden is 40 meters.

1. Find the dimensions of the garden (length and width).
2. Calculate the area of the garden.

Solution:

1. Find the dimensions of the garden (length and width):

   Let w be the width of the garden in meters.

   Then the length l of the garden is:

   l = w + 4 meters

   The formula for the perimeter P of a rectangle is:

   P = 2l + 2w

   Given:

   P = 40 meters

   Substitute l = w + 4 into the perimeter formula:

   40 = 2(w + 4) + 2w

   40 = 2w + 8 + 2w

   40 = 4w + 8

   40 - 8 = 4w

   32 = 4w

   w = ³²⁄₄

   w = 8 meters

   Now, find the length l:

   l = w + 4

   l = 8 + 4

   l = 12 meters

   So, the dimensions of the garden are:

   Width = 8 meters

   Length = 12 meters

2. Calculate the area of the garden:

   The formula for the area A of a rectangle is:

   A = l × w

   Given:

   l = 12 meters

   w = 8 meters

   So, the area A is:

   A = 12 × 8

   A = 96 square meters