The diagonal of a rectangle measures 26 cm the width of the rectangle is 24 cm find the length of the rectangle.
Pythagorean Theorem to the rescue!
a^2 + b^2 = c^2
24^2 + b^2 = 26^2
576 + b^2 = 676
b^2 = 676 - 576
b^2 = 100
b = 10
To find the length of the rectangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides (the width and length of the rectangle).
In this case, the width of the rectangle is 24 cm, and the diagonal (hypotenuse) is 26 cm. Let's label the length of the rectangle as 'l'.
Applying the Pythagorean theorem, we have:
Length^2 + Width^2 = Diagonal^2
l^2 + 24^2 = 26^2
Simplifying the equation:
l^2 + 576 = 676
Subtracting 576 from both sides:
l^2 = 676 - 576
l^2 = 100
Taking the square root of both sides:
√(l^2) = √100
l = 10
Therefore, the length of the rectangle is 10 cm.