QuestionTriangles and are similar. If has an area of 6 sq ft, find the area of with sides 12 ft and 4 ft.
Studdy Solution
STEP 1
Assumptions1. Triangles and are similar.
. The corresponding side lengths of triangles and are12 ft and4 ft respectively.
3. The area of is6 sq ft.
4. The area of similar triangles is proportional to the square of the ratio of their corresponding sides.
STEP 2
First, we need to find the ratio of the corresponding sides of the two triangles. This can be done by dividing the side length of by the side length of .
STEP 3
Now, plug in the given values for the side lengths of and to calculate the ratio.
STEP 4
Calculate the ratio.
STEP 5
Now that we have the ratio of the side lengths, we can find the ratio of the areas of the two triangles. This is done by squaring the ratio of the side lengths.
STEP 6
Plug in the value for the ratio to calculate the area ratio.
STEP 7
Calculate the area ratio.
STEP 8
Now that we have the area ratio, we can find the area of . This is done by multiplying the area of by the area ratio.
STEP 9
Plug in the values for the area of and the area ratio to calculate the area of .
STEP 10
Calculate the area of .
The area of is54 sq ft.
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