Question

In your living room, there is a large rectangular window with dimensions of 10 feet by 6 feet. You love the sunlight but would like to redesign the window so that it admits the same amount of light but is only 8 feet wide. How tall should your redesigned window be?

Short answer

Answer: The height of the redesigned window is 7.5 feet.

Step-by-step solution

Find the area of the original window

To find the area of the original window, we need to multiply the width by the height. The dimensions of the original window are 10 feet by 6 feet, so the area is (10 feet) × (6 feet) = 60 square feet.

Set up an equation for the area of the redesigned window

To find the area of the redesigned window, we know we need the width and height. We are given the width (which is 8 feet) but not the height. Let's call the height "h" for now, so the area of the new window is (8 feet) × (h feet).

Set up an equation relating the areas of the original and redesigned windows

Since we want the designed window to admit the same amount of light as before, we should set their areas equal: (10 feet) × (6 feet) = (8 feet) × (h feet)

Solve for h

We want to solve the equation for h, which represents the height of the redesigned window. Therefore, we need to isolate h in the equation. We have: 60 square feet = (8 feet) × (h feet). To isolate h, divide both sides of the equation by 8 feet: h = \frac{60 \text{ square feet}}{8 \text{ feet}} = 7.5\text{ feet}

Find the height of the redesigned window

The value of h that we found represents the height of the redesigned window. So, the redesigned window should be 7.5 feet tall.