In the given figure, DE ∥ BC. (i) Prove that ΔADE ΔABC. (ii) Given that AD = DB, calculate DE, if BC = 4.5 cm. (iii) Find . (iv) Find .

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KnowledgeBoat · Accepted Answer

(i) Considering ΔADE and ΔABC, ∠BAC = ∠DAE [Common angles] ∠ADE = ∠ABC [Corresponding angles are equal] ΔADE ΔABC (By A.A. axiom) Hence, proved that ΔADE ΔABC. (ii) Given, Since triangles ADE and ABC are similar so, ratio of their corresponding sides will be equal. Hence, the length of DE = 1.5 cm. (iii) We know that, The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Hence, . (iv) From figure, Area of trap.(BCED) = area(Δ ABC) - area(Δ ADE) Hence, .

Mathematics

In the given figure, DE ∥ BC. (i) Prove that ΔADE ΔABC. (ii) Given that AD = DB, calculate DE, if BC = 4.5 cm. (iii) Find . (iv) Find .

Similarity

Related Questions

In the given figure, BA ∥ DC. Show that ΔOAB ∼ ΔODC. If AB = 4 cm, CD = 3 cm, OC = 5.7 cm and OD = 3.6 cm, find OA and OB.

In the given figure, ∠ABC = 90° and BD ⟂ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, find BC.

Given that ΔABC ∼ ΔPQR.
(i) If ar(ΔABC) = 49 cm² and ar(ΔPQR) = 25 cm² and AB = 5.6 cm, find the length of PQ.
(ii) If ar(ΔABC) = 28 cm² and ar(ΔPQR) = 63 cm² and PR = 8.4 cm, find the length of AC.
(iii) If BC = 4 cm, QR = 5 cm and ar(ΔABC) = 32 cm² determine ar(ΔPQR).

The areas of two similar triangles are 48 cm² and 75 cm² respectively. If the altitude of the first triangle is 3.6 cm, find the corresponding altitude of the other.

Mathematics

In the given figure, DE ∥ BC. (i) Prove that ΔADE ΔABC. (ii) Given that AD = DB, calculate DE, if BC = 4.5 cm. (iii) Find . (iv) Find .

Similarity

Related Questions

In the given figure, BA ∥ DC. Show that ΔOAB ∼ ΔODC. If AB = 4 cm, CD = 3 cm, OC = 5.7 cm and OD = 3.6 cm, find OA and OB.

In the given figure, ∠ABC = 90° and BD ⟂ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, find BC.

Given that ΔABC ∼ ΔPQR.(i) If ar(ΔABC) = 49 cm2 and ar(ΔPQR) = 25 cm2 and AB = 5.6 cm, find the length of PQ.(ii) If ar(ΔABC) = 28 cm2 and ar(ΔPQR) = 63 cm2 and PR = 8.4 cm, find the length of AC.(iii) If BC = 4 cm, QR = 5 cm and ar(ΔABC) = 32 cm2 determine ar(ΔPQR).

The areas of two similar triangles are 48 cm2 and 75 cm2 respectively. If the altitude of the first triangle is 3.6 cm, find the corresponding altitude of the other.

Given that ΔABC ∼ ΔPQR.
(i) If ar(ΔABC) = 49 cm² and ar(ΔPQR) = 25 cm² and AB = 5.6 cm, find the length of PQ.
(ii) If ar(ΔABC) = 28 cm² and ar(ΔPQR) = 63 cm² and PR = 8.4 cm, find the length of AC.
(iii) If BC = 4 cm, QR = 5 cm and ar(ΔABC) = 32 cm² determine ar(ΔPQR).

The areas of two similar triangles are 48 cm² and 75 cm² respectively. If the altitude of the first triangle is 3.6 cm, find the corresponding altitude of the other.