MCQ
In $\triangle\text{ABC},\text{DE }||\text{ BC}$ such that $\frac{\text{AD}}{\text{DB}}=\frac{3}{5}. AC = 5.6\ cm$ then $AE =?$
- A$4.2\ cm$
- B$3.1\ cm$
- C$2.8\ cm$
- ✓$2.1\ cm$
✓
Answer
Correct option: D.
$2.1\ cm$
In $\triangle\text{ABC},\text{DE }\|\text{ BC}$
By Basic proportionality theorem,
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
$\Rightarrow\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{AC}-\text{AE}}$
$\Rightarrow\frac{3}{5}=\frac{\text{AE}}{\text{5.6}-\text{AE}}$
$\Rightarrow3(5.6-\text{AE})=5\text{AE}$
$\Rightarrow16.8-3\text{AE})=5\text{AE}$
$\Rightarrow8\text{AE}=16.8$
$\Rightarrow\text{AE}=2.1\text{cm}$
By Basic proportionality theorem,
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
$\Rightarrow\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{AC}-\text{AE}}$
$\Rightarrow\frac{3}{5}=\frac{\text{AE}}{\text{5.6}-\text{AE}}$
$\Rightarrow3(5.6-\text{AE})=5\text{AE}$
$\Rightarrow16.8-3\text{AE})=5\text{AE}$
$\Rightarrow8\text{AE}=16.8$
$\Rightarrow\text{AE}=2.1\text{cm}$
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
$\sec70^\circ\sin20^\circ+\cos20^\circ\text{cosec}\ 70^\circ=?$
→The areas of two similar triangles $\triangle\text{ABC}$ and $\triangle\text{DEF}$ are $144cm^2$ and $81cm^2$ respectively. If the longest side of larger $\triangle\text{ABC}$ be $36\ cm$, then the longest side of the smaller triangle $\triangle\text{DEF}$ is:
→The area of the sector of angle $\theta^\circ$ of a circle with radius $R$ is:
→If the perimeter of a circle is equal to that of a square, then the ratio of their areas is:
In a circle of radius $21\ cm.$ an arc subtends an angle of $60^\circ$ at the centre. The length of the arc is:
→From a point $Q$, the length of the tangent to a circle is $24\ cm$ and the distance of $Q$ from the centre is $25\ cm$. The radius of the circle is:
→In the given figure, quadrilateral $\text{ABCD}$ is circumscribed, touching the circle at $\text{P, Q, R}$ and $S$. If $\text{AP} = 6\ cm, \text{BP} = 5\ cm, \text{CQ} = 3\ cm$ and $\text{DR} = 4\ cm$, then the perimeter of quadrilateral $\text{ABCD}$ is:
→If the distance between the points $(4, p)$ and $(1, 0)$ is $5,$ then $p =$
→If points $(t, 2t), (-2, 6)$ and $(3, 1)$ are collinear, then $t =$
→________ number of tangent/s can be drawn from a point inside the circle.