quilt squares are cut on the diagonal to form triangle quilt pieces. the hypotenuse of the resulting triangles are 10 inches long, What is the side length of each piece?
x= 5sqrt2
To find the side length of each triangle quilt piece, we need to use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the hypotenuse is 10 inches long, so we can use it in the formula:
a² + b² = c²
where:
a and b are the lengths of the other two sides
c is the length of the hypotenuse
Since the triangle is a right triangle, we can assume one side to be the base of the quilt square and the other side to be the height of the quilt square. Therefore, we have:
a² + b² = 10²
Simplifying this equation will allow us to solve for the side length of each triangle quilt piece.
To find the side length of each quilt piece, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we know that the hypotenuse is 10 inches long, which we'll label as c. Let's label the other two sides of the right triangle as a and b.
The Pythagorean theorem can be written as:
c^2 = a^2 + b^2
In our case, c is 10 inches, so we have:
10^2 = a^2 + b^2
Simplifying:
100 = a^2 + b^2
Now, because the quilt squares are cut on the diagonal to form right triangles, we know that the two sides of each quilt piece are congruent. So, a = b. We can substitute a = b into the equation:
100 = a^2 + a^2
100 = 2a^2
Next, we can divide both sides of the equation by 2:
50 = a^2
To solve for a, we take the square root of both sides:
√50 = a
Using a calculator, we find that √50 is approximately equal to 7.07.
Therefore, the side length of each quilt piece is approximately 7.07 inches.
for a square of side s, the diagonal is s√2
So, you have s√2 = 10
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