If ΔABC~ΔPQR,A(ΔABC)=80,A(ΔPQR)=125, then fill in the blanks. A(ΔABC)/A(Δ. . . . )=80/125 ∴AB/PQ=......./.......
Answers
Answered by
34
Final Answer:
Steps:
1) We have,
ΔABC and ΔPQR ,similar to each other.
and
ar(ΔABC) = 80 sq. units
ar(ΔPQR) = 125 sq. units
2) We know that ,
Ratio of area of two similar triangles is equal to ratio of square of their corresponding sides.
![\frac{ar(ABC)}{ar(PQR)} = \frac{ AB^{2} }{ PQ^{2} } \\ \\ =\ \textgreater \ \frac{80}{125} = \frac{ AB^{2} }{ PQ^{2} } \\ \\ =\ \textgreater \ \frac{ AB^{2} }{ PQ^{2} } = \frac{16}{25} \\ \\ =\ \textgreater \ \frac{ AB }{ PQ } = \frac{4}{5} \frac{ar(ABC)}{ar(PQR)} = \frac{ AB^{2} }{ PQ^{2} } \\ \\ =\ \textgreater \ \frac{80}{125} = \frac{ AB^{2} }{ PQ^{2} } \\ \\ =\ \textgreater \ \frac{ AB^{2} }{ PQ^{2} } = \frac{16}{25} \\ \\ =\ \textgreater \ \frac{ AB }{ PQ } = \frac{4}{5}](https://tex.z-dn.net/?f=+%5Cfrac%7Bar%28ABC%29%7D%7Bar%28PQR%29%7D+%3D++%5Cfrac%7B+AB%5E%7B2%7D+%7D%7B+PQ%5E%7B2%7D+%7D+%5C%5C+%5C%5C+%3D%5C+%5Ctextgreater+%5C++++%5Cfrac%7B80%7D%7B125%7D+%3D+++%5Cfrac%7B+AB%5E%7B2%7D+%7D%7B+PQ%5E%7B2%7D+%7D++%5C%5C+%5C%5C+%3D%5C+%5Ctextgreater+%5C+++%5Cfrac%7B+AB%5E%7B2%7D+%7D%7B+PQ%5E%7B2%7D+%7D+%3D++%5Cfrac%7B16%7D%7B25%7D+%5C%5C+%5C%5C+%3D%5C+%5Ctextgreater+%5C+++%5Cfrac%7B+AB+%7D%7B+PQ+%7D+%3D++%5Cfrac%7B4%7D%7B5%7D+)
Hence,
![\boxed{\frac{AB}{PQ} = \frac{4}{5} } \boxed{\frac{AB}{PQ} = \frac{4}{5} }](https://tex.z-dn.net/?f=+%5Cboxed%7B%5Cfrac%7BAB%7D%7BPQ%7D+%3D+%5Cfrac%7B4%7D%7B5%7D+%7D)
Steps:
1) We have,
ΔABC and ΔPQR ,similar to each other.
and
ar(ΔABC) = 80 sq. units
ar(ΔPQR) = 125 sq. units
2) We know that ,
Ratio of area of two similar triangles is equal to ratio of square of their corresponding sides.
Hence,
Answered by
7
Answer:
u see in pic
Step-by-step explanation:
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