I need help solving this word problem

Question

The length of a rectangle is 4 inches more than its width. The area of the rectangle is 4 square inches . Write an equation that can be used to find the length and width . Use quadratic formula to find the length and width in radical form . Express the length and width to the nearest hundredth of an inch .

Answer 1

If the width is called w, how can you represent the length in terms of w? Then if you multiply these two expressions, w and the one you figure out you should get the area 4.

So w( ) = 4. You fill in the blank.

Then multiply out the left side, set the equation equal to 0 and solve for w.

Answer 2

Width = This is the measurement we're given no information for, so let's call it x

Length = We're told that the length is 4 more than the width, so if the width is x, the length will be x + 4

Width = x

Length = x + 4

We're told that the area is 4 square inches. Area of a rectangle can be found by multiplying the length (x + 4) by the width (x) so our equation is x (x + 4) = 4

Distribute the x into the parentheses and you get x² + 4x = 4

To use the quadratic formula you need your equation to be in the form of ax² + bx + c = 0

We can do that by moving the 4 on the right to the left side of the equation. We subtract 4 from both sides and get:

x² + 4x − 4 = 0

Now you can use the quadratic formula which is x = (-b ± √b² − 4ac) / 2a

Looking at our equation, x² + 4x - 4 = 0, we see that a = 1 b = 4 c = -4

Now that we know what each letter is we can plug the numbers into the quadratic formula:

(-4 ± √4² - 4(1)(-4)) / 2(1) −> −(-4 ± √16 − -16) / 2 −> (-4 ± √32) / 2 −> ....

When you're done simplifying you get that x = -2 − 2√2 and -2 + 2√2

The question however asks you do round to the nearest hundredth of an inch, so the answer should also be in decimal form. Plug it into the calculator and you will get .83 and -4.83 (rounded). We can reject the second value of x because it is negative and measurements cannot be negative. Therefore, x = .83 square inches.

Look back at the original measurements for length and width and plug in .83 for x

Length = x = .83 square inches

Width = x + 4 = 4.83 square inches

You can check you work by checking if the area of that rectangle is 4 (since we rounded up for x, the area will actually be a slightly greater than 4)

.83 x 4.83 = 4.0089 which when rounded to the nearest hundredth is 4!