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Solution for In the Following Figure, δAcb ~ δApq. If Bc = 8 Cm, Pq = 4 Cm, Ba = 6.5 Cm and Ap = 2.8 Cm, Find Ca and Aq. - CBSE Class 10 - Mathematics

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Question

In figure below ΔACB ~ ΔAPQ. If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm,
find CA and AQ. Also, find the area (ΔACB): area (ΔAPQ)

Solution

We have,

ΔACB ~ ΔAPQ

Then,

`"AC"/"AP"="CB"/"PQ"="AB"/"AQ"`                   [Corresponding parts of similar Δ are proportional]

`rArr"AC"/2.8=10/5=6.5/"AQ"`

`rArr"AC"/2.8=10/5` and `10/5=6.5/"AQ"`

`rArr"AC"=10/5xx2.8` and `"AQ"=6.5xx5/10`

⇒ AC = 5.6 cm and AQ = 3.25 cm

By area of similar triangle theorem

`("Area"(triangleACB))/("Area"(triangleAPQ))/"BC"^2/"PQ"^2`

`=10^2/5^2`

`=100/25`

= 4

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Solution In the Following Figure, δAcb ~ δApq. If Bc = 8 Cm, Pq = 4 Cm, Ba = 6.5 Cm and Ap = 2.8 Cm, Find Ca and Aq. Concept: Areas of Similar Triangles.
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