In Delta ABC,A-M-B,A-N-C and overline{MN} par | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) According to the Basic Proportionality Theorem (Thales Theorem),if a line is drawn parallel to one side of a triangle to intersect the other two s

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(D) According to the Basic Proportionality Theorem (Thales Theorem),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.Since $\overline{MN} \parallel \overline{BC}$,we have:$\frac{AM}{MB} = \frac{AN}{NC}$Substituting the given values:$\frac{x+1}{2x-2} = \frac{2x+2}{3x+1}$Cross-multiplying:$(x+1)(3x+1) = (2x-2)(2x+2)$$3x^2 + x + 3x + 1 = 4x^2 - 4$$3x^2 + 4x + 1 = 4x^2 - 4$Rearranging the terms to form a quadratic equation:$x^2 - 4x - 5 = 0$Factoring the quadratic equation:$(x-5)(x+1) = 0$This gives $x = 5$ or $x = -1$.Since the length of a side cannot be negative,$x$ must be positive.Therefore,$x = 5$.

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = x+1$,$MB = 2x-2$,$AN = 2x+2$ and $NC = 3x+1$,find the value of $x$.

Similar Questions

In triangles $PQR$ and $MST$,$\angle P = 55^{\circ}$,$\angle Q = 25^{\circ}$,$\angle M = 100^{\circ}$ and $\angle S = 25^{\circ}$. Is $\triangle QPR \sim \triangle TSM$? Why?

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. Prove that $\frac{1}{BM^2} = \frac{1}{AB^2} + \frac{1}{BC^2}$.

In a rhombus,the diagonals measure $10$ and $24$. Then,the length of each side of the rhombus is...........

In rectangle $HIJK$,$HJ = 13$ and $HI = 5$. Then,the perimeter of rectangle $HIJK$ is.......

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 12$,$BD = 9$ and $BC = 21$,find $AC$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module