How much shorter is to walk diagonally across a rectangular field that is 24cm long and 18cm width than along two of its adjacent sides.
Thanks for the answer
To calculate the difference in length between walking diagonally across a rectangular field and walking along two of its adjacent sides, we can use the Pythagorean theorem.
The diagonal is the hypotenuse of a right triangle, and the two sides adjacent to the diagonal are the rectangle's length and width.
Let's denote the length as a and the width as b. In this case, a = 24 cm and b = 18 cm.
According to the Pythagorean theorem, the length of the diagonal (d) can be calculated using the formula:
d = √(a^2 + b^2)
Substituting the values we have:
d = √(24^2 + 18^2)
= √(576 + 324)
= √900
= 30 cm
So the length of the diagonal is 30 cm.
To find the difference in length between walking diagonally and walking along two adjacent sides, we subtract the sum of the length and width from the diagonal's length:
Difference = diagonal - (length + width)
= 30 cm - (24 cm + 18 cm)
= 30 cm - 42 cm
= -12 cm
The result is -12 cm, indicating that walking diagonally across the rectangular field is 12 cm shorter than walking along two of its adjacent sides.
To find out how much shorter it is to walk diagonally across the rectangular field compared to walking along two of its adjacent sides, we need to calculate the lengths of both paths and then find the difference between them.
Let's start by calculating the length of walking along two adjacent sides. In a rectangle, the opposite sides are equal in length, so we can calculate the length of walking along two adjacent sides by adding the lengths of two adjacent sides.
Given that the length of the rectangle is 24cm and the width is 18cm, we add the length of both adjacent sides:
Length of walking along two adjacent sides = 24cm + 24cm = 48cm
Next, let's calculate the length of walking diagonally across the rectangle. We can use the Pythagorean theorem to find the length of the diagonal. In a rectangle, the diagonal, length, and width form a right-angled triangle. The Pythagorean theorem states that the square of the length of the diagonal is equal to the sum of the squares of the length and width.
Using the given values:
Length^2 + Width^2 = Diagonal^2
24cm^2 + 18cm^2 = Diagonal^2
576cm^2 + 324cm^2 = Diagonal^2
900cm^2 = Diagonal^2
Taking the square root of both sides:
Diagonal = sqrt(900cm^2)
Diagonal = 30cm
Now we have the length of walking diagonally across the field, which is 30cm.
To find the difference in length between these two paths, we subtract the length of walking along two adjacent sides from the length of walking diagonally across the field:
Difference = Diagonal - Length of walking along two adjacent sides
Difference = 30cm - 48cm
Difference = -18cm
Therefore, walking diagonally across the field is 18cm shorter than walking along two of its adjacent sides.
Walking along two of its adjacent sides: 24 + 18 = 42cm
Draw the diagonal (to form two triangles). Find the hypotenuse of one of the triangles to find the diagonal. Use pythagoras theorem:
c = sqrt[a^2 + b^2]
= sqrt[24^2 + 18^2]
= 30cm
Therefore, it is 12cm shorter to walk diagonally across.