Area equals length times the width

Question

the Floor has an area of 84 square feet. The shape of a rectangle whose length is 2 feet less than the width. Find the length and width.

Answer 1

Question: the Floor has an area of 84 square feet. The shape of a rectangle whose length is 2 feet less than the width. Find the length and width.

Answer: We will be using the formula Area= length times width

Step 1: Choose a variable for one of the unknows. Our unknows are length and width.

We will consider width to be x.

Step 2: Create an expression for the other unknown.

The problem mentions, " length is 2 feet less than the width". So if width is x, length is x-2.

Step 3: Plug in the values into the area formula.

A= l * w

84= (x-2)(x)

84 = x² -2x

-84 -84

—————

0 = x² -2x -84

Step 4: Use the quadratic formula. The a value is 1, b value is -2 and c is -84 for the quadratic equation.

-b ± √b² -4ac

x = ——————

2a

-(-2) ± √(-2)² -4(1)(-84)

x = ———————————

2(1)

2 ± √4 + 336

x = ——————

2

2 ± √340

x = ————

2

2 ± 18.439

x = ——————

2

2 + 18.439 2 - 18.439

x = —————— or ——————

2 2

x = 10.2195 or -8.2195

But width cannot be negative, so width = 10.22 feet rounded to the nearest hundredth.

Step 5: Find length by replacing x by 10.22.

Length = x- 2

Length = 10.22 -2

Length = 8.22 feet