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Winston takes a rectangular piece of fabric and makes a diagonal cut from one corner to the opposite corner. The cut he makes is 10 inches long and the width of the fabric is 8 inches. What is the fabric’s length?
inches
To find the length of the rectangular piece of fabric, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the diagonal cut) is equal to the sum of the squares of the other two sides (the width and the length).
Here, the diagonal cut (hypotenuse) is 10 inches, and the width is 8 inches. We can denote the length as ( l ).
According to the Pythagorean theorem:
[
l^2 + 8^2 = 10^2
]
Now, calculate ( 8^2 ) and ( 10^2 ):
[
l^2 + 64 = 100
]
Now, solve for ( l^2 ):
[
l^2 = 100 – 64
]
[
l^2 = 36
]
Taking the square root of both sides gives us:
[
l = 6
]
So, the length of the fabric is 6 inches.