A builder cuts a rectangular hole in a ceiling to install an exhaust fan. The width is 3 in. less than the length and the area is 180 in². Find the length and width of the hole.

Area of a rectangle = l * w

A = Area of a rectangle

l = length

w = width

In our problem,

l = x

w = x - 3

A = 180 square inches

Plug our numbers into the area formula of a rectangle

180 square inches = x(x-3)

Distribute the x into (x-3)

180 square inches = x^2 - 3x

subtract 180 from both sides

0 = x^2 - 3x -180.

Factor the express on the left side of the equation

0 = (x-15) (x+12).

Set each term equal to zero and solve for x

x+12 = 0.

Subtract 12 from both sides

x = -12 <--- lengths of a rectangle cannot be negative, therefore, we need to check the other term we factored.

set x-15 equal to zero

x-15 = 0.

Add 15 to both sides

x = 15.

We know l = x so now we know that the length i = 15 inches.

We also know that the width = length - 3

w = 15 - 3

w = 12

The width is 12 inches and the length is 15 inches

29 is the correct answer

step-by-step explanation:

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98