The side of a square is 15 cm. Calculate the length of its diagonal. (1dp)
d^2 = 2s^2
Shape geometry: Square
For a square, all four sides are the same length.
If you draw a diagonal line from the lower left corner to the upper right corner, you'll have 2 right triangles.
The diagonal line is called the hypothenuse of a right triangle.
The formula to calculate the length of diagonal (Hypothenuse) is called the Pythagorean Theorem:
a^2 + b^2= c^2
a= height of triangle
b= base of triangle
c= diagonal/hypotenuse of of triangle
Solution:
a=15cm
b=15cm
Find c:
15^2+15^2 = c^2
c=sqrt(15^2+15^2)
More information:
https://www.mathsisfun.com/pythagoras.html
To calculate the length of the diagonal of a square, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In a square, the diagonal is the hypotenuse of two right triangles formed by dividing the square into two equal right triangles. These right triangles have sides that are half the length of the square's sides.
Let's calculate the length of the diagonal using the Pythagorean theorem.
1. Determine the length of one side of the square. In this case, it is given as 15 cm.
2. Divide the length of the side by 2 to get the length of one side of the right triangle formed inside the square. In this case, 15 cm / 2 = 7.5 cm.
3. Use the Pythagorean theorem to find the length of the diagonal. The formula is:
diagonal² = (one side of the right triangle)² + (one side of the right triangle)²
diagonal² = 7.5 cm² + 7.5 cm²
diagonal² = 2 * (7.5 cm)²
diagonal² = 2 * 56.25 cm²
diagonal² = 112.5 cm²
4. Take the square root of both sides to find the length of the diagonal.
diagonal = √(112.5 cm²)
diagonal ≈ 10.61 cm (rounded to 1 decimal place)
So, the length of the diagonal of the square with a side length of 15 cm is approximately 10.61 cm.