∆ABC ∽ ∆PQR, A(∆ABC) = 16, A(∆PQR) = 25, then find the value of ratio AB : PQ. / ∆ABC ∽ ∆PQR, A(∆ABC) = 16, A(∆PQR) = 25, तर AB : PQ या गुणोत्तराची किंमत काढा. *
Answers
Given:
∆ABC ∽ ∆PQR
Area of ∆ABC = 16
Area of ΔPQR = 25
To find:
The value of the ratio of AB:PQ
Solution:
Since we are given that ΔABC and ΔPQR are similar to each other, so we can state the following theorem:
The ratio of the two similar triangles is equal to the square of the ratio of their corresponding sides.
here,
AB and PQ are the corresponding sides of the similar triangles
∴
substituting the given values of area of ΔABC & area of ΔPQR
⇒
taking square root on both sides
⇒
⇒
⇒
Thus, the value of ratio of AB : PQ is 4 : 5.
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Answer:
Given:
∆ABC ∽ ∆PQR
Area of ∆ABC = 16
Area of ΔPQR = 25
To find:
The value of the ratio of AB:PQ
Solution:
Since we are given that ΔABC and ΔPQR are similar to each other, so we can state the following theorem:
The ratio of the two similar triangles is equal to the square of the ratio of their corresponding sides.
here,
AB and PQ are the corresponding sides of the similar triangles
∴ \frac{Area(\triangle ABC)}{Area(\triangle PQR)} = (\frac{AB}{PQ})^{2}
Area(△PQR)
Area(△ABC)
=(
PQ
AB
)
2
substituting the given values of area of ΔABC & area of ΔPQR
⇒ \frac{16}{25} = (\frac{AB}{PQ})^{2}
25
16
=(
PQ
AB
)
2
taking square root on both sides
⇒ \sqrt{ \frac{16}{25}} = \sqrt{(\frac{AB}{PQ})^{2}}
25
16
=
(
PQ
AB
)
2
⇒ \frac{4}{5} = \frac{AB}{PQ}
5
4
=
PQ
AB
⇒ \bold{AB:PQ = 4:5}AB:PQ=4:5
Thus, the value of ratio of AB : PQ is 4 : 5.