Question
Find the value of x for which $DE || AB$ in:
✓
Answer
Given $DE || AB$
$\therefore\frac{\text{CD}}{\text{AD}}=\frac{\text{CE}}{\text{BE}}$ [by basic proportionality theorem]
$\Rightarrow\frac{\text{x}+3}{3\text{x}+4}=\frac{\text{x}}{3\text{x}+4}$
$\Rightarrow (x + 3)(3x +4) = x(3x + 19)$
$\Rightarrow 3x^2 + 4x + 9x + 12 = 3x^2 + 19x$
$\Rightarrow 19x - 13x = 12$
$\Rightarrow 6x = 12$
$\therefore\text{x}=\frac{12}{6}=2$
Hence, the required value of x is 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 marks obtained out of $50$, by $102$ students in a Physics test are given in the frequency table below:
Find the average number of marks.
→|
Marks (x)
|
$15$
|
$20$
|
$22$
|
$24$
|
$25$
|
$30$
|
$33$
|
$38$
|
$45$
|
|
Frequncy (f)
|
$5$
|
$8$
|
$11$
|
$20$
|
$23$
|
$18$
|
$13$
|
$3$
|
$1$
|
Show taht the following points are collinear:A(2, -2), B(-3, 8) and C(-1, 4)
The common tangents AB and CD to two circles with centres O and O’ intersect at E between their centres. Prove that the points O, E and O’ are collinear.
Divide 56 in four parts in A.P. such that the ratio of the product of their extremes to the product of their means is 5 : 6.
A girl of heigh 90cm is walking away from the base of a lamp-post at a speed of 1.2m/sec. If the lamp is 3.6m above the ground, find the length of her shadow after 4 seconds.
$A B C D$ is a parallelogram with vertices $A\left(x_1, y_1\right), B\left(x_2, y_2\right)$ and $C\left(x_3, y_3\right)$. Find the coordinates of the fourth vertex $D$ in terms of $x _1, x _2, x _3, y _1, y _2$ and $y _3$.
→Solve the following quadratic equation:$\frac{2}{\text{x}^2}-\frac{5}{\text{x}}+2=0$
→In $\triangle\text{ABC},\text{D}$ is the midpoint of BC and $\text{AE}\perp\text{BC}.$ If $\text{AC}>\text{AB},$ show that.
$\text{AB}^2=\text{AD}^2-\text{BC}.\text{DE}+\frac{1}{4}\text{BC}^2.$
→$\text{AB}^2=\text{AD}^2-\text{BC}.\text{DE}+\frac{1}{4}\text{BC}^2.$
In a right triangle ABC, right angled at C, if $\angle\text{B} = 60^\circ$ and AB = 15 units. Find the remaining angles and sides.
→Prove that $7 \sqrt { 5 }$ is irrational.
→