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Chapter 4: Q. 356 (page 480)

In the following exercises,translate to a system of equations and solve.

Becca is hagging a 28 foot floral garland on the two sides and top of a pergola to prepare for a wedding. The height is four feet less than the width.Find the width and height of the pergola.

Short Answer

Expert verified

The height and width of the pergola are 8 and 12 respectively.

Step by step solution

01

Step 1.Given information

Given,

Height is four feet less than width,

Let h represents the height of the pergola

Let w represents the width of the pergola.

That means,h=w-4.

02

Step 2.Find the height and width of the pergola.

Becca is hagging a 28 foot floral garland on the two sides and top of a pergola to prepare for a wedding.

That means 2h+w=28.

Substitute h=w-4in equation 2h+w=28and solve for w.

2(w-4)+w=282w-8+w=283w-8=283w=36w=363w=12

Substitute w=12 in the 2h+w=28and solve for h.

2h+12=282h=28-122h=16h=8

03

Step 3.Checking

First substitute h=8,w=12 into the equation h=w-4

h=w-48=12-48=8

this is true.

Also substitute h=8,w=12 into the equation 2h+w=28

2(8)+12=2816+12=2828=28

This is also true.

Therfore,The height and width of the pergola are 8 and 12 respectively.

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