The blueprint of a triangular patio has side lengths 4.5 in., 4.5 in., and 6.25 in. If the shorter sides of the actual patio are each 13.5 ft long, how long is the third side?
(Simplify your answer.)
The blueprint of a triangular patio has side lengths 4.5 in., 4.5 in., and 6.25 in. If the shorter sides of the actual patio are each 13.5 ft long, how long is the third side
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To solve for the length of the third side of the actual patio, we can use a proportion based on the given side lengths of the triangular patio and the actual lengths.
The original side lengths are:
– a = 4.5 in.
– b = 4.5 in.
– c = 6.25 in.
The shorter sides of the actual patio (corresponding to a and b) are each 13.5 ft long.
First, we find the scaling factor from the original blueprint to the actual patio using one of the shorter sides:
Scaling factor = Actual side length / Original side length
Scaling factor = 13.5 ft / 4.5 in.
Next, we need to convert 13.5 ft into inches for consistency:
13.5 ft = 13.5 x 12 in. = 162 in.
Now we calculate the scaling factor:
Scaling factor = 162 in. / 4.5 in. = 36.
Now we use this scaling factor to find the length of the third side:
Actual length of the third side = Original third side length x scaling factor
Actual length of the third side = 6.25 in. x 36 = 225 in.
To convert the answer back into feet:
225 in. ÷ 12 in/ft = 18.75 ft.
So, the length of the third side of the actual patio is 18.75 ft.