A rectangular jewelry store has a perimeter of 124 feet. Its area is 880 square feet. What are the dimensions of the store? ___ feet by ___ feet

Answer 1

First, let's make sure you know what the vocabulary of the problem means:

Perimeter: the sum of all the sides

Area = length • width (In this case the short side multiplied by the long side of the rectangle)

Dimension: a measurement

This problem is shown by the following equations:

Perimeter: 2x + 2y = 124

Area: x • y = 880

There are several ways to solve this, let's look at two.

1) You could plug the equations into a demos-type graphing calculator and see where the lines cross for your answer. This shows they cross at (22,40) and (40,22) so the sides are 22 and 40.

2) Because it is a system you can use substitution to solve. See below.

Step 1:

2x + 2y = 124

x • y = 880 → y = 880/x

Step 2:

2x + 2(880/x) = 124

Step 3:

2x + ( 2 • _880_) =

1 + (1 • x ) =

Step 4:

x(2x + 1760/x) = (124)x

2x² + 1760 = 124x

2x² - 124x + 1760 = 0 This is a quadratic equation.

Step 5:

Put these numbers into the quadratic formula.

𝑥= −(−124)±√(−124)2−4(2)(1760)

2(2)

Step 6:

𝑥= −(−124)±√15376−14080

4

Step 7:

x= 124±36

4

x= 22 OR x=40