A rectangle of length of 10 cm has diagonals of length 12 cm.
Calculate the width of the rectangle.
Form a right triangle with the hypotenuse as 12, one of the sides as 10, the third side is therefore, using Pythagoras theorem,
√(12²-10²)
=√(144-100)
=√44.
a^2 + b^2 = c^2
10^2 + c^2 = 12^2
100 + c^2 = 144
c^2 = 44
c = 6.633 cm
dssc
To calculate the width of the rectangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the rectangle forms a right triangle with one of the diagonals as the hypotenuse.
Let's call the width of the rectangle 'w', and the length 'l'.
We have the following information:
Length (l) = 10 cm
Diagonal (d) = 12 cm
Using the Pythagorean theorem, we can solve for 'w':
w^2 + l^2 = d^2
Substituting the known values:
w^2 + 10^2 = 12^2
w^2 + 100 = 144
Subtracting 100 from both sides:
w^2 = 44
Taking the square root of both sides:
w = sqrt(44)
Calculating the square root of 44:
w ≈ 6.63 cm
Therefore, the width of the rectangle is approximately 6.63 cm.