Question
In the given figure, $\angle\text{ABC}=90^\circ$ and $\text{BD} \perp\text{AC.}$ If AB = 5.7cm, BD = 3.8cm and CD = 5.4cm, find BC.
✓
Answer
We have, $\angle\text{ABC}=90^\circ$ and $\text{BD}\perp\text{AC}$
In $\triangle\text{ABC}$ and $\triangle\text{BDC}$
$\angle\text{ABC}=\angle\text{BDC}$ [Each 90°]
$\angle\text{C}=\angle\text{C}$ [Commom]
Then, $\triangle\text{ABC}\sim\triangle\text{BDC}$ [By AA similarity]
$\therefore\frac{\text{AB}}{\text{BD}}=\frac{\text{BC}}{\text{DC}}$ [Corresponding parts of similar $\triangle$ are proportional]
$\Rightarrow\frac{5.7}{3.8}=\frac{\text{BC}}{5.4}$
$\Rightarrow\text{BC}=\frac{5.7}{3.8}\times8.1\text{cm}$
In $\triangle\text{ABC}$ and $\triangle\text{BDC}$
$\angle\text{ABC}=\angle\text{BDC}$ [Each 90°]
$\angle\text{C}=\angle\text{C}$ [Commom]
Then, $\triangle\text{ABC}\sim\triangle\text{BDC}$ [By AA similarity]
$\therefore\frac{\text{AB}}{\text{BD}}=\frac{\text{BC}}{\text{DC}}$ [Corresponding parts of similar $\triangle$ are proportional]
$\Rightarrow\frac{5.7}{3.8}=\frac{\text{BC}}{5.4}$
$\Rightarrow\text{BC}=\frac{5.7}{3.8}\times8.1\text{cm}$
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
Two men on either side of the cliff 80m high observes the angles of a elevation of the top of the cliff to be 30° and 60° respectively. Find the distance between the two men.
An AP consists of 50 terms of which $3^{\text {rd }}$ term is 12 and the last term is 106 . Find the $29^{\text {th }}$ term.
→Find the value of k, if the points A(7, -2), B(5, 1) and C(3, 2k) are collinear.
The daily income of a sample of 50 employees are tabulated as follows:
Find the mean daily income of employees.
|
Income (in Rs.)
|
1-200
|
201-400
|
401-600
|
601-800
|
|
Number of employees
|
14
|
15
|
14
|
7
|
A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in figure. Find:
- the total length of the silver wire required.
- the area of each sector of the brooch.
"https://pg-data.sgp1.digitaloceanspaces.com/chapter_wise/5245/image106.gif" style="height: 107px; width: 120px;" />
In the following, determine whether the given quadratic equation have real root and if so, find the root:
$16x^2 = 24x + 1$
→$16x^2 = 24x + 1$
In a $\triangle\text{ABC, D}$ and E are points on the sides AB and AC respectively. For the following cases show that DE || BC:
AB = 10.8cm, BD = 4.5cm, AC = 4.8cm and AE = 2.8cm.
→AB = 10.8cm, BD = 4.5cm, AC = 4.8cm and AE = 2.8cm.
The following are quadratic equations in x?
$\text{x}^2-\frac{1}{\text{x}^2}=5$
→$\text{x}^2-\frac{1}{\text{x}^2}=5$
Which term of the $AP. 53, 48, 43,...$ is the first negative term?
→In the given figure, a quadrilateral $\text{ABCD}$ is drawn to circumscribe a circle such that its sides $AB, BC, CD$ and $AD$ touch the circle at $P, Q, R $ and $S$ respectively. If $AB = x \ cm, BC = 7 \ cm, CR = 3 \ cm$ and $AS = 5 \ cm,$ find $x$.
→