Given triangle ABC is similar to triangle PQR, if the ratio of area triangle ABC to area triangle PQR is 121:225, then find the ratio of PR to AC
Answers
Answer:
Given:
Triangle ABC is similar to triangle PQR,
The ratio of area triangle ABC to area triangle PQR is 121:225
To find:
The ratio of PR to AC
Form a theorem:
The ratio of the areas of two similar triangles is equivalent to the ratio of the squares of their corresponding sides.
So,
\dfrac{121}{225} = (\dfrac{PR}{AC})^{2}
225
121
=(
AC
PR
)
2
\implies (\dfrac{11}{15})^{2} = (\dfrac{PR}{AC})^{2}⟹(
15
11
)
2
=(
AC
PR
)
2
\implies (\dfrac{11}{15})= (\dfrac{PR}{AC})⟹(
15
11
)=(
AC
PR
)
Hence,
The ratio of PR o AC is 11:15
More Information
In such a similar question, when the side ratio is given and the ratio of the area of the triangle is asked then square the given side ratio.
When the ratio of the area of the similar triangle is given and the question asked to find the ratio of sides then take out the square root of the ratio of the area of the triangles.
Step-by-step explanation:
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