IF length of rectangle is 20 & breadth 5cm, find the side of square which is equiangular with rectangle.
Strange wording, since all squares and rectangles are "equiangular".
Did you mean , find the side of the square which has the same area as the rectangle?
then
s^2 = 20(5) = 100
s = 10 cm
Why did the rectangle go to the doctor? Because it was feeling a little "square"!
Now, to answer your question - if the length of the rectangle is 20 cm and the breadth is 5 cm, to find the side of a square that is equiangular with the rectangle, we can use the formula L/B = side/side, where L is the length, B is the breadth, and side is the side length of the square.
Given L = 20 cm and B = 5 cm, we can set up the equation:
20/5 = side/side
Dividing both sides by side, we get:
4 = 1
Uh oh! This equation doesn't make sense! It seems like there's been a mix-up somewhere.
But don't worry, I'm always here to make you smile, even if I can't find the solution this time. Keep that sense of humor handy, and maybe someone else can help you with the correct answer.
To find the side length of the square that is equiangular with the given rectangle, we need to determine the length of the diagonal of the rectangle first. Then we can set this diagonal as the diagonal of the square since they are equiangular. Finally, we can calculate the side length of the square using the diagonal.
Step 1: Calculate the diagonal of the rectangle using the Pythagorean theorem.
The Pythagorean theorem states that for a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, a = length of the rectangle = 20 cm
b = breadth of the rectangle = 5 cm
Using the Pythagorean theorem, we can find the diagonal (d) of the rectangle:
d^2 = a^2 + b^2
d^2 = 20^2 + 5^2
d^2 = 400 + 25
d^2 = 425
Step 2: Find the square root of 425 to get the diagonal of the square.
d = √425
d ≈ 20.62 cm
Step 3: Since the diagonal of the square is equal to 20.62 cm, all sides of the square will be equal.
Therefore, the side length of the square that is equiangular with the given rectangle is approximately 20.62 cm.
To find the side of the square that is equiangular with the given rectangle, we need to determine the length of the common diagonal of the rectangle and the square.
First, let's calculate the diagonal of the rectangle. The diagonal can be found using the Pythagorean theorem, which states that the square of the hypotenuse (diagonal) of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the length of the rectangle is 20 cm, and the breadth is 5 cm. We can use these values as the two sides of a right triangle, with the diagonal as the hypotenuse.
Using the Pythagorean theorem:
Diagonal^2 = length^2 + breadth^2
Diagonal^2 = 20^2 + 5^2
Diagonal^2 = 400 + 25
Diagonal^2 = 425
To find the length of the diagonal, we take the square root of both sides:
Diagonal = √425
Diagonal ≈ 20.62 cm (rounded to two decimal places)
Now that we know the length of the diagonal of the rectangle, we can conclude that the side of the equiangular square will also be 20.62 cm.