In the adjoining figure, ΔACB &sim; ∆APQ. If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm find the area (∆ACB) : area (∆APQ).

In the Adjoining Figure, δAcb ∼ ∆Apq. If Bc = 10 Cm, Pq = 5 Cm, Ba = 6.5 Cm and Ap = 2.8 Cm Find the Area (∆Acb) : Area (∆Apq). - Mathematics

In the adjoining figure, ΔACB ∼ ∆APQ. If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm find the area (∆ACB) : area (∆APQ).

Sum

∆ACB ∼ ∆APQ.
Then, `"area (∆ACB)"/"area (∆APQ)" = "BC"^2/"PQ"^2`
= `(10)^2/(5)^2`
= `(100)/(25)`
= `(4)/(1)`
Required ratio is 4 : 1.

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Areas of Similar Triangles Are Proportional to the Squares on Corresponding Sides

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Chapter 13 Similarity
Figure Based Questions | Q 1

In the given figure, DE || BC, AE = 15 cm, EC = 9 cm, NC = 6 cm and BN = 24 cm.

In ΔABC, angle ABC is equal to twice the angle ACB, and bisector of angle ABC meets the opposite side at point P. Show that: AB × BC = BP × CA

In the following figure, ABCD to a trapezium with AB ‖ DC. If AB = 9 cm, DC = 18 cm, CF = 13.5 cm, AP = 6 cm and BE = 15 cm, Calculate: PE

In the following figure, ABCD to a trapezium with AB || DC. If AB = 9 cm, DC = 18 cm, CF = 13.5 cm, AP = 6 cm and BE = 15 cm, Calculate: AF

In the following figure, AB, CD and EF are perpendicular to the straight line BDF.

If AB = x and CD = z unit and EF = y unit, prove that : `1/x + 1/y = 1/z`

In the following figure, ∠AXY = ∠AYX. If `(BX)/(AX) = (CY)/(AY)`, show that triangle ABC is isosceles.

In the figure given below, AB || EF || CD. If AB = 22.5 cm, EP = 7.5 cm, PC = 15 cm and DC = 27 cm.

Calculate :

In the given figure, AB and DE are perpendiculars to BC.

If AB = 6 cm, DE = 4 cm and AC = 15 cm. Calculate CD.

Triangles ABC and DEF are similar.
If area (ΔABC) = 16 cm, area (ΔDEF) = 25 cm² and BC = 2.3 cm find EF.

Triangles ABC and DEF are similar.
If area (ΔABC) = 9 cm², area (ΔDEF) = 64 cm² and BC = 5·1 cm find AB.