Question

5
ABC and ADE are two similar triangles. IfAD: DB=2:3 and
DE=5 cm, calculate length of BC. Find the altitude of ABCif
the altitude of ADE is h.​

Answer 1

Given :- ABC and ADE are two similar triangles. If AD : DB = 2:3 and DE = 5 cm . Calculate length of BC. Find the altitude of ABC if the altitude of ADE is h cm. ?

Solution :-

we know that, If two triangles are similar, then the ratio of any two corresponding segments (such as altitudes, medians, or angle bisectors) equals the ratio of any two corresponding sides.

given that, ∆ABC is similar to ∆ADE .

so,

→ AB / AD = BC / DE = AC / AE = (Altitude of ∆ABC) / (Altitude of ∆ADE) .

now, given that,

• AD : DB = 2 : 3
• AD : AB = 2 : (2+3) = 2 : 5

then,

→ AB / AD = BC / DE = AC / AE = (Altitude of ∆ABC) / (Altitude of ∆ADE) = 5/2

also , given,

DE = 5 cm.

therefore,

→ BC / DE = 5 / 2

→ BC / 5 = 5 / 2

→ 2BC = 5 * 5

→ 2BC = 25

→ BC = 12.5 cm (Ans.)

now, given ,

Altitude of ADE = h.

hence,

→ (Altitude of ∆ABC) / (Altitude of ∆ADE) = 5/2

→ (Altitude of ∆ABC) / h = 5/2

→ 2 * Altitude of ∆ABC = 5h

→ Altitude of ∆ABC = (5h/2) cm. (Ans.)

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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