Advertisements
Advertisements
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
APPEARS IN
RELATED QUESTIONS
If ∆ABC ~ ∆DEF such that area of ∆ABC is 16cm2 and the area of ∆DEF is 25cm2 and BC = 2.3 cm. Find the length of EF.
D and E are points on the sides AB and AC respectively of a ∆ABC such that DE || BC and divides ∆ABC into two parts, equal in area. Find
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2CD, find the ratio of the areas of triangles AOB and COD.
In Figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that `(ar(ABC))/(ar(DBC)) = (AO)/(DO)`
Triangles ABC and DEF are similar If AC = 19cm and DF = 8 cm, find the ratio of the area of two triangles.
In ΔABC, D and E are the mid-points of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC
ABCD is a trapezium in which AB || CD. The diagonals AC and BD intersect at O. Prove that: (i) ΔAOB and ΔCOD (ii) If OA = 6 cm, OC = 8 cm,
Find:(a) `("area"(triangleAOB))/("area"(triangleCOD))`
(b) `("area"(triangleAOD))/("area"(triangleCOD))`
The perpendicular from A on side BC of a Δ ABC meets BC at D such that DB = 3CD. Prove that 2AB2 = 2AC2 + BC2.
If ΔABC is similar to ΔDEF such that 2 AB = DE and BC = 8 cm then EF is equal to ______.
If ΔABC ∼ ∆PQR and AB : PQ = 2 : 3, then find the value of `(A(triangleABC))/(A(trianglePQR))`.
