Question
What values of x will make $DE || AB$ in the given figure?
✓
Answer
$In the figure, in $\triangle\text{ABC},$$
$DE || AB$
$\therefore\frac{\text{AD}}{\text{DC}}=\frac{\text{BE}}{\text{EC}}$
$\Rightarrow\frac{3\text{x}+19}{\text{x}+3}=\frac{3\text{x}+4}{\text{x} }$
$\Rightarrow x(3x + 19) = (x + 3)(3x + 4)$
$\Rightarrow 3x^2 + 19x = 3x^2 + 4x + 9x + 12$
$\Rightarrow 3x^2 + 19x - 3x^2 - 4x - 9x = 12$
$\Rightarrow6\text{x}=12\Rightarrow\text{x}=\frac{12}{6}=2$
$\therefore$ $x = 2$
$DE || AB$
$\therefore\frac{\text{AD}}{\text{DC}}=\frac{\text{BE}}{\text{EC}}$
$\Rightarrow\frac{3\text{x}+19}{\text{x}+3}=\frac{3\text{x}+4}{\text{x} }$
$\Rightarrow x(3x + 19) = (x + 3)(3x + 4)$
$\Rightarrow 3x^2 + 19x = 3x^2 + 4x + 9x + 12$
$\Rightarrow 3x^2 + 19x - 3x^2 - 4x - 9x = 12$
$\Rightarrow6\text{x}=12\Rightarrow\text{x}=\frac{12}{6}=2$
$\therefore$ $x = 2$
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
66 cubic cm of silver is drawn into a wire 1mm in diameter. Calculate the length of the wire in metres.
In the following figure, $OABC$ is a square of side 7cm. If $OAPC$ is a quadrant of a circle with centre $O$, then find the area of the shaded region. $\Big(\text{Use }\pi=\frac{22}{7}\Big).$
→If a circle touches the side $B C$ of a triangle $A B C$ at $P$ and extended sides $A B$ and $A C$ at $Q$ and $R$, respectively, prove that $AQ=\frac{1}{2}(BC+CA+AB)$
→Very-Short-Answer Questions:
If the product of two numbers is 1050 and their HCF is 25, find their LCM.
If the product of two numbers is 1050 and their HCF is 25, find their LCM.
A line intersects $y -$axis and $x -$axis at point $P$ and $Q,$ respectively. If $R(2,5)$ is the mid$-$point of line segment $PQ ,$ then find the coordinates of $P$ and $Q.$
→Write the ratio in which the line segment joining the points A(3, -6) and B(5, 3) is divided by x-axis.
If $x=a \cos ^3 \theta, y=b \sin ^3 \theta$, prove that $\left(\frac{x}{a}\right)^{2 / 3}+\left(\frac{y}{b}\right)^{2 / 3}=1$
→Find the area of the segment shown in Fig., if radius of the circle is $21 \ cm$ and $\angle A O B=120^{\circ}$ $($Use $\pi=\frac{22}{7} )$
→The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Two dice are rolled together. Find the probability of getting such numbers on the two dice whose product is 12.