B Solve.
(1) Δ ABC Δ PQR. Α(Δ ABC) : A(Δ PC
AC:PR.
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Answer:
The ratio AC: PR is 9:7.
Step-by-step explanation:
Given information: ∆ ABC ~ ∆ PQR. A(∆ ABC) : A(∆ PQR) =81:49
If two triangles are similar, then the square of the ratio of their corresponding sides is proportional to the ratio of the area of both triangles.
\dfrac{A(\triangle ABC)}{A(\triangle PQR)}=\dfrac{AC^2}{PR^2}
A(△PQR)
A(△ABC)
=
PR
2
AC
2
\dfrac{81}{49}=(\dfrac{AC}{PR})^2
49
81
=(
PR
AC
)
2
Taking square root on both sides.
\sqrt{\dfrac{81}{49}}=\dfrac{AC}{PR}
49
81
=
PR
AC
\dfrac{9}{7}=\dfrac{AC}{PR}
7
9
=
PR
AC
Therefore, the ratio AC: PR is 9:7.
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