Answer: 20 feet by 20 feet.
Step-by-step explanation:
1. You know that is the original measure of one side. Since it is a square, all its sides are equal.
2. Therefore, to solve the problem you only need to solve for , as you can see below:
- You have that:
- Then, you obtain the following quadratic equation:
- Apply the Quadratic formula to solve it:
- Then, you obtain:
3. The dimensions cannot be negative, therefore, the answer is: 20 feet by 20 feet.
<u>Answer:</u>
<u>Step-by-step explanation:</u>
We know from the question that the student earned $12.50 <em>per hour</em>.
Using this information, we can say that if the student worked for <em>h </em>hours, they would make a total of 12.50 × <em>h </em>dollars.
We also know that the total money they earned is $2500.75.
∴ Therefore, we can set up the following equation:
From here, if we want to, we can find the number of hours worked by simply making <em>h</em> the subject of the equation and evaluating:
<em>h </em>=<em> </em>
= 200.6 hours
Answer:
Dimensions of the rug = 13 ft × 26 ft
Step-by-step explanation:
Dimensions of the room = 21 ft × 34 ft
Area of the room = 21 × 34 = 714 ft²
Cynthia wants to leave a uniform strip of floor around the rug.
Let the width of the rug = x ft
Then the dimensions of the rug will be = (21- 2x)ft × (34 - 2x)ft
Area of the rug = (21 - 2x)×(34 - 2x) square feet
338 = (21 - 2x)×(34 - 2x)
338 = 714 - 68x - 42x + 4x²
4x² - 110x + 714 - 338 = 0
4x² - 110x + 376 = 0
2x² - 55x + 188 = 0
2x² - 47x - 8x + 188 = 0
x(2x - 47) - 8(x - 47) = 0
(x - 4)(2x - 47) = 0
x = 4,
For x = 23.5 area of the rug will be negative.
Therefore, x = 4 ft will be the width of the rug.
Dimensions of the rug will be 13 ft × 26 ft.