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In ∆ABC ,D and E are points on the sides AB and AC respectively such that DE is parallel to BC , 1) If AD= 2.5 cm ,BD = 3cm ,AE = 3.75 cm find length of AC. 2) If AD = 4 cm , AE =8cm ,DB =x – 4 cm ,EC =3x -19 cm , find x 3) I f AD =2cm ,BD = 4cm , show that BC = 3 DE

User Pindare
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1 Answer

12 votes
12 votes

Answer:

1). AC=8.25cm

2). DB=7cm & EC=14cm

3). See Explanation

Explanation:

According To the Question,

Given That, In ∆ABC, D and E are points on the sides AB and AC respectively such that DE is parallel to BC.

1). If AD= 2.5 cm ,BD = 3cm ,AE = 3.75 cm find length of AC.

Well we can apply Basic proportionality Theorem.

Since DE ║ BC ⇒ Sides are proportional and the angles are equal.

⇒ AD / BD = AE / EC

⇒ 2.5 / 3 = 3.75 / EC

On Solving we get,

⇒ EC * 2.5 = 3.75 * 3

⇒ EC * 2.5 = 11.25

⇒ EC = 11.25 / 2.5

⇒ EC = 4.5 cm

Thus,

AC = AE + EC

⇒ AC = 3.75 + 4.50

AC = 8.25 cm

Hence the measure of AC is 8.5 cm.

2). If AD = 4 cm , AE =8cm ,DB =x – 4 cm ,EC =3x -19 cm

Well we can apply Basic proportionality Theorem.

Since DE ║ BC ⇒ Sides are proportional and the angles are equal.

⇒ AD / BD = AE / EC

⇒ 4 / (x-4) = 8 / (3x-19)

on solving we get,

⇒ 3x-19 = 2(x-4)

⇒ 3x-19 = 2x-8

x=11

Thus, DB =x–4 ⇒ 11-4 ⇒ DB=7cm

And, EC =3x-19 ⇒ 3×11-19 ⇒ EC=14cm

3). If AD=2cm , BD= 4cm , show that BC = 3 DE

Thus, AB = AD + DB = 2+4 = 6cm

Well we can apply Basic proportionality Theorem.

Since DE ║ BC ⇒ Sides are proportional and the angles are equal.

⇒ AD/AB = DE / BC

⇒ 2 / 6 = DE / BC

on solving we get

BC = 3 DE Hence, Proved

User Shimon Doodkin
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