Final answer:
The rug will cost $720. To find the cost, we need to determine the area of the rug by finding its length using the Pythagorean theorem. The length of the rug is 15 feet, so the area is 120 square feet. Multiplying the area by the cost per square foot gives us a total cost of $720.
Step-by-step explanation:
To find the cost of the rug, we need to determine its area. The rug is shaped like a rectangle with a width of 8 feet. Let's assume the length of the rug is 'x' feet. We can use the Pythagorean theorem to find 'x'. The diagonal length of 17 feet is the hypotenuse of a right triangle, where the width and length of the rug are the legs. So, we have:
82 + x2 = 172
Simplifying the equation, we get:
64 + x2 = 289
Subtracting 64 from both sides:
x2 = 289 - 64
x2 = 225
Take the square root of both sides:
x = 15
Therefore, the length of the rug is 15 feet.
To find the area of the rug, we multiply the width and length:
Area = width × length = 8 feet × 15 feet = 120 square feet
Since the rug costs $6 per square foot, the total cost of the rug would be:
Total Cost = Area × Cost per square foot = 120 square feet × $6 per square foot = $720