The length of a rectangle is 8 feet more than it's worth. The area of the rectangle is 84 ft.². Find its Length and width.

Question

Mathematics

Marble

12 May, 16:53

The length of a rectangle is 8 feet more than it's worth. The area of the rectangle is 84 ft.². Find its Length and width.

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Answers (1)

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Rudy Pace · Answer 1

Answer: 100 i think, but am not sure.

Step-by-step explanation:

The formula for area of a rectangle is A=l*w. Since the area is 84, then you can use the A=l*w formula. 84 = x (x+8) would be the equation to solve for x.

Now, you need to put the equation in standard form. So, x2 + 8x - 84 = 0.

Since you can't solve this quadratic using factoring, you need to complete the square.

To complete the square you need to add 84 to both sides. Now you have x2 + 8x = 84. Take the coefficient for the x term (8) and divide by 2. Now square it. That would be 42, so 16. Now you have x2 + 8x + 16 = 100.

Factor x2 + 8x + 16, so (x+4) 2 = 100

If you use the square root property, you have x+4 = 10. Therefore, x = 6 (the short side) and 14 is the long side.