Question
In $\triangle ABC , D$ and $E$ are the points on the sides AB and AC respectively such that DE||BC. If AD = 6x - 7, DB = 4x - 3, AE = 3x - 3 and EC = 2x - 1, find the value of x.
✓
Answer
Given: In $\triangle ABC , DE \| BC$. Also $AD =6 x -7, DB =4 x -3, AE =3 x -3$ and $EC =2 x -1$
By basic proportionality theorem,
$\frac{A D}{D B}=\frac{A E}{E C}$
$\Rightarrow \frac{6 x-7}{4 x-3}=\frac{3 x-3}{2 x-1}$
$\Rightarrow(6 x-7)(2 x-1)=(3 x-3)(4 x-3)$
$\Rightarrow 12 x^2-6 x-14 x+7=12 x^2-9 x-12 x+9$
$\Rightarrow-20 x+7=-21 x+9$
$\Rightarrow-20 x+21 x=9-7$
$\Rightarrow x=2$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The volume of a right circular cylinder with its height equal to the radius is$25\frac{1}{7}\text{cm}^3$ Find the height of the cylinder.
→Prove the following:
$\sin\theta\sin(90^\circ-\theta)-\cos\theta\cos(90^\circ-\theta)=0$
→$\sin\theta\sin(90^\circ-\theta)-\cos\theta\cos(90^\circ-\theta)=0$
In the figure, PA and PB are tangents to the circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PB = 10cm and CQ = 2cm, what is the length PC?
A steel wire when bent in the form of a square encloses an area of $121 cm^2$. If the same wire is bent in the form of a circle, find the area of the circle.
→Solve the following quadratic equation:$4 - 11x = 3x^2$
→Short-Answer Questions:If $\cot\text{A}=\frac{4}{5}$ prove that $\frac{(\sin\text{A}+\cos\text{A})}{(\sin\text{A}-\cos\text{A})}=9$
→In the adjoining figure, find AC.
In the following, find the value of k for which the given value is a solution of the given equation:
$x^2 - x(a + b) + k = 0, x = a$
→$x^2 - x(a + b) + k = 0, x = a$
Find the value of $' k\ '$ so that the quadratic equation $3 x^2-5 x-2 k=0$ has real and equal roots.
→Solve the pair of linear equations by substitution method: 3x – y = 3; 9x – 3y = 9