A projector screen is 3.5 ft tall and 6 ft wide. You want to project a...

A projector screen is 3.5 ft tall and 6 ft wide. You want to project a photo that is 4 in tall by 6 in wide. What are the dimensions of the image of the largest photo that will fit on the screen?

Solutions

Expert Solution

12 inches = 1 foot. Converting the projectors dimension into inches we have 3.5 ft = 3.5 * 12 = 42 inches and 6 ft = 6 * 12 = 72 inches.

We can either increase the length of the photo upto 42 inches or the breadth upto 72 inches, whichever is smaller, but the same number of times needs to be applied equally to length and beadth.

Case1: Increase length to the maximum possible from 4 inches to 42 inches, which is an increase by 10.5 times. This is the max length.

The breadth is increased by the same number of times = 6 * 10.5 = 63 inches

Therefore in this case the maxuimum dimensions are 42 inches by 63 inches.

Case 2: Increase breadth to the maximum from 6 inches to 72 inches, which is an increase by 12 times.

The length therefore becomes 4 * 12 = 48 inches, which then will not fit on the screen.

Therefore the dimensions of the largest photo = 42 inch tall (42/12 = 3.5 ft) and 63 inches wide (63/12 = 5.25 ft)

milcah answered 1 year ago

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