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A muralist is painting the side wall of a building. The wall is shaped like a rectangle that is $60$ feet long and has a diagonal length of $68$ feet. If a gallon of paint can cover $800$ square feet, how many gallons will the muralist use? $\newline$ ____ gallons $\newline$

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Solve proportions: word problems

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Q. A muralist is painting the side wall of a building. The wall is shaped like a rectangle that is

60

feet long and has a diagonal length of

68

feet. If a gallon of paint can cover

800

square feet, how many gallons will the muralist use?

\newline

____ gallons

\newline

Calculate Wall Height: Calculate the height of the wall using the Pythagorean theorem, given the diagonal and length of the rectangle. $\newline$ $height^2 + length^2 = diagonal^2$ $\newline$ $height^2 + 60^2 = 68^2$ $\newline$ $height^2 + 3600 = 4624$ $\newline$ $height^2 = 4624 - 3600$ $\newline$ $height^2 = 1024$ $\newline$ $height = \sqrt{1024}$ $\newline$ $height = 32$ feet
Calculate Wall Area: Calculate the area of the wall using the length and height. $\newline$ Area = $\text{length} \times \text{height}$ $\newline$ Area = $60 \, \text{feet} \times 32 \, \text{feet}$ $\newline$ Area = $1920 \, \text{square feet}$
Determine Paint Gallons: Determine the number of gallons of paint needed using the area and coverage per gallon. $\newline$ Number of gallons = $\frac{\text{Area}}{\text{Coverage per gallon}}$ $\newline$ Number of gallons = $\frac{1920 \text{ square feet}}{800 \text{ square feet per gallon}}$ $\newline$ Number of gallons = $2.4$

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