Defence Exam > Defence Questions > A square and an equilateral triangle have the...
Start Learning for Free
A square and an equilateral triangle have the same perimeter, If the diagonal of the square is 6√2 cm, then what is the area of the triangle?
- a)12√2 cm2
- b)12√3 cm2
- c)16√2 cm2
- d)16√3 cm2
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A square and an equilateral triangle have the same perimeter, If the d...
Diagonal of the square = √2 × side of the square
∴ Side of the square = 6√2/√2 = 6 cm
4 × Side of the square = 3 × Side of the triangle
4 × 6 = 3 × Side of the triangle
∴ Side of the equilateral triangle = 8 cm
Area of the equilateral triangle = √3/4 × side2
⇒ √3/4 × 82 = 16√3 cm2
∴ Side of the square = 6√2/√2 = 6 cm
4 × Side of the square = 3 × Side of the triangle
4 × 6 = 3 × Side of the triangle
∴ Side of the equilateral triangle = 8 cm
Area of the equilateral triangle = √3/4 × side2
⇒ √3/4 × 82 = 16√3 cm2
Most Upvoted Answer
A square and an equilateral triangle have the same perimeter, If the d...
Let's denote the side length of the square as $s$ and the side length of the equilateral triangle as $t$.
The perimeter of the square is equal to four times its side length, so it is $4s$.
The perimeter of the equilateral triangle is equal to three times its side length, so it is $3t$.
Since the square and the equilateral triangle have the same perimeter, we have $4s = 3t$.
We are given that the diagonal of the square is 6. In a square, the diagonal is equal to the product of the side length and $\sqrt{2}$, so we have $s\sqrt{2} = 6$. Dividing both sides of this equation by $\sqrt{2}$ gives us $s = \frac{6}{\sqrt{2}} = \frac{6\sqrt{2}}{2} = 3\sqrt{2}$.
Substituting this value of $s$ into the equation $4s = 3t$, we get $4(3\sqrt{2}) = 3t$. Simplifying this equation gives us $12\sqrt{2} = 3t$. Dividing both sides of this equation by 3 gives us $4\sqrt{2} = t$.
So, the side length of the equilateral triangle is $t = 4\sqrt{2}$.
In summary, the side length of the square is $s = 3\sqrt{2}$ and the side length of the equilateral triangle is $t = 4\sqrt{2}$.
The perimeter of the square is equal to four times its side length, so it is $4s$.
The perimeter of the equilateral triangle is equal to three times its side length, so it is $3t$.
Since the square and the equilateral triangle have the same perimeter, we have $4s = 3t$.
We are given that the diagonal of the square is 6. In a square, the diagonal is equal to the product of the side length and $\sqrt{2}$, so we have $s\sqrt{2} = 6$. Dividing both sides of this equation by $\sqrt{2}$ gives us $s = \frac{6}{\sqrt{2}} = \frac{6\sqrt{2}}{2} = 3\sqrt{2}$.
Substituting this value of $s$ into the equation $4s = 3t$, we get $4(3\sqrt{2}) = 3t$. Simplifying this equation gives us $12\sqrt{2} = 3t$. Dividing both sides of this equation by 3 gives us $4\sqrt{2} = t$.
So, the side length of the equilateral triangle is $t = 4\sqrt{2}$.
In summary, the side length of the square is $s = 3\sqrt{2}$ and the side length of the equilateral triangle is $t = 4\sqrt{2}$.
|
Explore Courses for Defence exam
|
|
Similar Defence Doubts
A square and an equilateral triangle have the same perimeter, If the diagonal of the square is 6√2 cm, then what is the area of the triangle?a)12√2 cm2b)12√3 cm2c)16√2 cm2d)16√3 cm2Correct answer is option 'D'. Can you explain this answer?
Question Description
A square and an equilateral triangle have the same perimeter, If the diagonal of the square is 6√2 cm, then what is the area of the triangle?a)12√2 cm2b)12√3 cm2c)16√2 cm2d)16√3 cm2Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A square and an equilateral triangle have the same perimeter, If the diagonal of the square is 6√2 cm, then what is the area of the triangle?a)12√2 cm2b)12√3 cm2c)16√2 cm2d)16√3 cm2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square and an equilateral triangle have the same perimeter, If the diagonal of the square is 6√2 cm, then what is the area of the triangle?a)12√2 cm2b)12√3 cm2c)16√2 cm2d)16√3 cm2Correct answer is option 'D'. Can you explain this answer?.
A square and an equilateral triangle have the same perimeter, If the diagonal of the square is 6√2 cm, then what is the area of the triangle?a)12√2 cm2b)12√3 cm2c)16√2 cm2d)16√3 cm2Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A square and an equilateral triangle have the same perimeter, If the diagonal of the square is 6√2 cm, then what is the area of the triangle?a)12√2 cm2b)12√3 cm2c)16√2 cm2d)16√3 cm2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square and an equilateral triangle have the same perimeter, If the diagonal of the square is 6√2 cm, then what is the area of the triangle?a)12√2 cm2b)12√3 cm2c)16√2 cm2d)16√3 cm2Correct answer is option 'D'. Can you explain this answer?.
Solutions for A square and an equilateral triangle have the same perimeter, If the diagonal of the square is 6√2 cm, then what is the area of the triangle?a)12√2 cm2b)12√3 cm2c)16√2 cm2d)16√3 cm2Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
Download more important topics, notes, lectures and mock test series for Defence Exam by signing up for free.
Here you can find the meaning of A square and an equilateral triangle have the same perimeter, If the diagonal of the square is 6√2 cm, then what is the area of the triangle?a)12√2 cm2b)12√3 cm2c)16√2 cm2d)16√3 cm2Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A square and an equilateral triangle have the same perimeter, If the diagonal of the square is 6√2 cm, then what is the area of the triangle?a)12√2 cm2b)12√3 cm2c)16√2 cm2d)16√3 cm2Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A square and an equilateral triangle have the same perimeter, If the diagonal of the square is 6√2 cm, then what is the area of the triangle?a)12√2 cm2b)12√3 cm2c)16√2 cm2d)16√3 cm2Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A square and an equilateral triangle have the same perimeter, If the diagonal of the square is 6√2 cm, then what is the area of the triangle?a)12√2 cm2b)12√3 cm2c)16√2 cm2d)16√3 cm2Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A square and an equilateral triangle have the same perimeter, If the diagonal of the square is 6√2 cm, then what is the area of the triangle?a)12√2 cm2b)12√3 cm2c)16√2 cm2d)16√3 cm2Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Defence tests.
|
|
Explore Courses for Defence exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup