Question

If a storm window has an area of 640 square inches, what is the equation to find the dimensions when the window is 20 inches higher than it is wide (x represents height)?

Answer 1

To find the dimensions of the storm window, use the equation x(x+20) = 640 and solve for x. The dimensions of the storm window are 16 inches by 36 inches.

Step-by-step explanation:

The equation to find the dimensions of the storm window is:

x(x+20) = 640

First, distribute the x:

x^2 + 20x = 640

Then, rearrange the equation into standard form:

x^2 + 20x - 640 = 0

Next, factor the quadratic equation:

(x + 40)(x - 16) = 0

Set each factor equal to zero and solve for x:

x + 40 = 0 or x - 16 = 0

x = -40 or x = 16

Since the dimensions cannot be negative, the only valid solution is x = 16.

Therefore, the dimensions of the storm window are 16 inches by 36 inches.

Answer 2

area = width * height
since the window is 20 inches higher than the width:
width +20 = height

640 = width * width+20
640 = width^2 +20*width
width^2 +20*width - 640 = 0
width = 17.203
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Double Check
if width = 17.203 then height = 37.203
area = 17.203 * 37.203 = 640 square inches Correct!!