Algebra 2 Word Problem Help.

Question

The length of a particular rectangle is equal to about 1.28 times the width. An architect wants to design the base of a building to be a rectangle whose sides are in the same ratio as those of the given rectangle. If the perimeter of the base is to be 800 feet, what must the dimensions of the base be?

Answer 1

We have 2 unknowns, length and width, so we need 2 equations to answer this.

Eq. 1: Let l=length

              w=width

              l=1.28w

Eq. 2: Perimeter=P=800 ft

          P=2(l+w)

Using the substitution method, replace l with 1.28w in Eq. 2 and solve for w:

          P=2(1.28w+w)

          800=2(2.28w)

          400=2.28w      divide both sides by 2

          400/2.28=w     divide both sides by 2.28

          175.44=w

Use this value of w in Eq. 1 to find the length, l:

          l=1.28w

          l=1.28(175.44)

          l=224.56

Check your answers by putting them back into each equation and evaluate:

         l=1.28w                        P=2(l+w)

         224.56=1.28(175.44)    800=2(224.56+175.44)       

         224.56=224.56             800=2(400)

         Check!                          800=800

                                            Check!

Your answer is length = 224.56ft

                      width = 175.44 ft