Question

Help!!!

In a ∆ABC, D and E are points on the sides of AB and AC respectively such that DE || BC.

x) If AD = x, DB = 5x - 3, AE = 4x - 3 and EC = 3x - 1, find the value of x.

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Answer 1

Basic Proportionality Theorem (BPT) :-

 

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

Explaination:-

Given:-

Δ ABC &  DE || BC , AD = (8x -7), DB = 5x – 3, AE= 4x – 3 and EC = 3x -1

Solution:-

So, AD/DB=AE/ EC

[By using basic proportionality  Theorem]

Then,( 8x–7)/(5x–3) = (4x–3)/(3x–1)

(8x – 7)(3x – 1) = (5x – 3)(4x – 3)

24x² – 8x - 21x + 7 = 20x² - 15x -12x + 9

24x² – 29x + 7 = 20x² - 27x + 9

24x² - 20x² – 29x + 27x + 7 - 9= 0

4x² – 2x – 2 = 0

2(2x² – x – 1) = 0

2x² – x – 1 = 0

2x² – 2x + x – 1 = 0

[By Middle term splitting]

2x(x – 1) + 1(x – 1) = 0

(x – 1)(2x + 1) = 0

x = 1 or x = -1/2

[Since the side of triangle can never be negative]

Therefore, x = 1.

Hence,the value of x is 1 cm.

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Hope it helps u : )

Answer 2

This is your answer

Hope it will help you.