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Byju's Answer

Standard X

Mathematics

Converse of BPT

In a Δ ABC,...

Question

In a $Δ A B C$ , $D$ and $E$ are points on the sides $A B$ and $A C$ respectively such that $D E | | B C$ .
If $A D = x, D B = x - 2, A E = x + 2$ and $E C = x - 1$ , find the value of $x$ .

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Solution

$\begin{matrix} I n Δ A B C & Δ A D E ∠ A = ∠ A & ∠ A B C = ∠ A D E ∴ Δ A B C \sim Δ A D E [A A s i m i l a r i t y] \frac{A B}{A D} = \frac{A C}{A E} \frac{A B}{A D} - 1 = \frac{A C}{A E} - 1 \frac{A B - A D}{A D} = \frac{A C - A E}{A E} \Rightarrow \frac{D B}{A D} = \frac{E C}{A E} \Rightarrow \frac{x - 2}{x} = \frac{x - 1}{x + 2} (x - 2) (x + 2) = x (x - 1) x^{2} - 4 = x^{2} - x ∴ x = 4 \end{matrix}$

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In a ΔABC, D and E are points on the sides AB and AC respectively such that DE||BC.If AD=x,DB=x−2,AE=x+2 and EC=x−1, find the value of x.

InΔABC&ΔADE∠A=∠A&∠ABC=∠ADE∴ΔABC∼ΔADE[AAsimilarity]ABAD=ACAEABAD−1=ACAE−1AB−ADAD=AC−AEAE⇒DBAD=ECAE⇒x−2x=x−1x+2(x−2)(x+2)=x(x−1)x2−4=x2−x∴x=4

In a $Δ A B C$ , $D$ and $E$ are points on the sides $A B$ and $A C$ respectively such that $D E | | B C$ .
If $A D = x, D B = x - 2, A E = x + 2$ and $E C = x - 1$ , find the value of $x$ .