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What is the length of the diagonal of a square whose perimeter is equal to the perimeter of an equilateral triangle of side 4 cm?
- a)4. 24 cm
- b)4.04 cm
- c)4.14 cm
- d)4.64
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
What is the length of the diagonal of a square whose perimeter is equa...
Perimeter of an equilateral triangle
= 4 + 4 + 4 = 12 cm
Perimeter of square = 12 cm ⇒ 4 × side = 12 ⇒ Side = 3 cm.
∴ Length of diagonal =
= 4 + 4 + 4 = 12 cm
Perimeter of square = 12 cm ⇒ 4 × side = 12 ⇒ Side = 3 cm.
∴ Length of diagonal =
Most Upvoted Answer
What is the length of the diagonal of a square whose perimeter is equa...
As per the question,
Perimeter of Equilateral ∆ = perimeter of that square
so, 3×4 = "
12 = perimeter of the square
and then side will also be 3cm
Now , In the figure of square
you will see the formation of right angled ∆
so, at there you have to apply the formula of Pythagoras theorem i. e, diagonal^2(hypotenuse) = side^2(altitude) +
side^2(base)
d^2= 3^2 + 3^2
d^2= 9+9
d= √18
then, d= approx 4.24 cm____
_____
Perimeter of Equilateral ∆ = perimeter of that square
so, 3×4 = "
12 = perimeter of the square
and then side will also be 3cm
Now , In the figure of square
you will see the formation of right angled ∆
so, at there you have to apply the formula of Pythagoras theorem i. e, diagonal^2(hypotenuse) = side^2(altitude) +
side^2(base)
d^2= 3^2 + 3^2
d^2= 9+9
d= √18
then, d= approx 4.24 cm____
_____
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Community Answer
What is the length of the diagonal of a square whose perimeter is equa...
Perimeter of the square and equilateral triangle:
The perimeter of a square is given by 4 x side length, and the perimeter of an equilateral triangle is given by 3 x side length. In this case, both perimeters are equal, so we have:
4 x side length of the square = 3 x side length of the equilateral triangle
4s = 3 x 4
4s = 12
s = 3 cm
Length of the diagonal of the square:
To find the length of the diagonal of the square, we can use the Pythagorean theorem. In a square, the diagonal forms a right triangle with two sides equal to the side length of the square. Therefore, the length of the diagonal (d) can be calculated as:
d^2 = s^2 + s^2
d^2 = 2s^2
d = sqrt(2s^2)
d = sqrt(2 x 3^2)
d = sqrt(18)
d ≈ 4.24 cm
Therefore, the length of the diagonal of the square is approximately 4.24 cm, which corresponds to option A.
The perimeter of a square is given by 4 x side length, and the perimeter of an equilateral triangle is given by 3 x side length. In this case, both perimeters are equal, so we have:
4 x side length of the square = 3 x side length of the equilateral triangle
4s = 3 x 4
4s = 12
s = 3 cm
Length of the diagonal of the square:
To find the length of the diagonal of the square, we can use the Pythagorean theorem. In a square, the diagonal forms a right triangle with two sides equal to the side length of the square. Therefore, the length of the diagonal (d) can be calculated as:
d^2 = s^2 + s^2
d^2 = 2s^2
d = sqrt(2s^2)
d = sqrt(2 x 3^2)
d = sqrt(18)
d ≈ 4.24 cm
Therefore, the length of the diagonal of the square is approximately 4.24 cm, which corresponds to option A.
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What is the length of the diagonal of a square whose perimeter is equal to the perimeter of an equilateral triangle of side 4 cm?a)4. 24 cmb)4.04 cmc)4.14 cmd)4.64Correct answer is option 'A'. Can you explain this answer?
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