Question
$\triangle\text{ABC}\sim\triangle\text{DEF}$ and their areas are respectively $100\ cm^2 $ and $49\ cm^2.$ If the altitude of $\triangle\text{ABC}$ is $5\ cm$, the corresponding altitude of $\triangle\text{DEF}.$
✓
Answer
It is given that $\triangle\text{ABC}\sim\triangle\text{DEF}.$
Therefore, the ratio of the areas of these triangles will be equal to the ratio of squares of their corresponding sides.
Also, the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding altitudes.
Let the altitude of $\triangle\text{ABC}$ be $AP,$ drawn from $A$ to $BC$ to meet $BC$ at $P$ and the altitude of $\triangle\text{DEF}$ be $DQ,$ drawn from $D$ to meet EF at $Q$
Then,
$\frac{\text{ar}(\triangle\text{ACB})}{\text{ar}(\triangle\text{DEF})}=\frac{\text{AP}^2}{\text{DQ}^2}$
$\Rightarrow\frac{100}{49}=\frac{\text{5}^2}{\text{DQ}^2}$
$\Rightarrow\frac{100}{49}=\frac{\text{25}}{\text{DQ}^2}$
$\Rightarrow\text{DQ}^2=\frac{49\times25}{100}$
$\Rightarrow\text{DQ}=\sqrt{\frac{49\times25}{100}}$
$\Rightarrow\text{DQ}=3.5\text{cm}$
Hence, the altitude of $\triangle\text{DEF}$ is $3.5\ cm$
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
→→→→→→→
A die is rolled twice. Find the probability that:
5 will come up both the times.
5 will come up both the times.
Evaluate the following:
If A = 60° and B = 30°, verify that:
$\tan(\text{A}-\text{B})=\frac{\tan\text{A}-\tan\text{B}}{1+\tan\text{A}\tan\text{B}}$
→If A = 60° and B = 30°, verify that:
$\tan(\text{A}-\text{B})=\frac{\tan\text{A}-\tan\text{B}}{1+\tan\text{A}\tan\text{B}}$
A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of getting:
-
A queen.
-
A diamond.
-
A king or an ace.
-
A red ace.
If (2p - 1), 7, 3p are in AP, find the value of p.
Following is the breakup of expenditure of a family on different times of consumption.
Draw a pie diagram of the above data.
| Item | Food | Clothing | Rent | Education | Fuel | Medicine | Miscellaneous |
| Expenditure in ₹ | 1600 | 200 | 600 | 150 | 100 | 80 | 270 |
A motor boat can travel 30km upstream and 28km downstream in 7 hours. It can travel 21km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.
The frequency distribution table of agriculture holdings in a village is given below:
Find the modal agriculture holdings of the village.
|
Area of land (in hactares):
|
1-3
|
3-5
|
5-7
|
7-9
|
9-11
|
11-13
|
|
Number of families:
|
20
|
45
|
80
|
55
|
40
|
12
|
Two natural numbers differ by $3$ and their product is $504$. Find the numbers.
→A two-digit number is $4$ times the sum of its digits and twice the product of its digit. Find the number.
→