A circle is inscribed in a square whose perimeter is 40 cm, what is the diameter of the circle?
40/4 = 10
Perimeter Of square = circumference of circle
Then,
Circumference of circle = 2¢ r
40 = 2 * 22/7 * r
140 = 22 * r
r = 140/22
r = 70/11
D = 140/11
To find the diameter of the inscribed circle, we can use the relationship between the square's perimeter and the circle's diameter.
Step 1: Use the formula for the perimeter of a square, which is P = 4s, where P is the perimeter and s is the length of each side of the square. In this case, the perimeter is given as 40 cm, so we have:
40 = 4s
Step 2: Solve for the length of each side of the square by dividing both sides of the equation by 4:
40/4 = s
10 = s
Step 3: The diameter of the inscribed circle is equal to the length of each side of the square. Therefore, the diameter of the circle is 10 cm.
To find the diameter of the circle inscribed in the square, we need to use the properties of a square and circle.
Since the perimeter of the square is given as 40 cm, we know that the sum of all four sides of the square is 40 cm. As the square has four equal sides, each side of the square is equal to 40 cm divided by 4, which is 10 cm.
In a square, the diagonals are always equal. The diagonal of the square is also the diameter of the inscribed circle. Therefore, the diameter of the circle is equal to the diagonal of the square.
To find the diagonal of the square, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the sides of the right-angled triangle are half the length of the square's side, which is 5 cm (because each side is 10 cm).
Using the Pythagorean theorem, we can calculate the diagonal of the square:
diagonal^2 = (side^2 + side^2)
diagonal^2 = (5 cm)^2 + (5 cm)^2
diagonal^2 = 25 cm^2 + 25 cm^2
diagonal^2 = 50 cm^2
Taking the square root of both sides, we find:
diagonal = √50 cm
diagonal ≈ 7.07 cm
Therefore, the diameter of the circle inscribed in the square is approximately 7.07 cm.