Question
A rectangular piece of cardboard is 40m wide . The length of the diagonal is 50m what is the area of the board
Answers
GPT 3.5
Let the length of the rectangular cardboard be denoted by 'x'. Using the Pythagorean theorem, we can set up an equation to solve for 'x'.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the lengths of the other two sides. So we can write:
x^2 + (40m)^2 = (50m)^2
Expanding and simplifying:
x^2 + 1600m^2 = 2500m^2
Subtracting 1600m^2 from both sides:
x^2 = 2500m^2 - 1600m^2
x^2 = 900m^2
Taking the square root of both sides:
x = 30m
So the length of the rectangular piece of cardboard is 30m.
To find the area of the board, we multiply the length by the width:
Area = length * width = 30m * 40m = 1200m^2.
Therefore, the area of the rectangular cardboard is 1200 square meters.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the lengths of the other two sides. So we can write:
x^2 + (40m)^2 = (50m)^2
Expanding and simplifying:
x^2 + 1600m^2 = 2500m^2
Subtracting 1600m^2 from both sides:
x^2 = 2500m^2 - 1600m^2
x^2 = 900m^2
Taking the square root of both sides:
x = 30m
So the length of the rectangular piece of cardboard is 30m.
To find the area of the board, we multiply the length by the width:
Area = length * width = 30m * 40m = 1200m^2.
Therefore, the area of the rectangular cardboard is 1200 square meters.