Question

This is a question that I would prefer to be answered quickly-ish and I would like it if there was an explanation.

The area of a rectangular room is 84 ft^2. the length of the room is 8ft greater than the width. The situation can be represented as W^2-8w-84=0. What is the width?

Answer 1

Explanation:

You can start by drawing a diagram. Then, you need to pick the shorter side and designate it as "x". The longer side must be "x+8".

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.

I hope that helps.