A rectangular city block measures 105 by 88 meters.The city council wants to divide the block into two triangles of equal area. What is the length of the hypotenuse of each triangular area?( I already found the area of the whole rectangle and the area of each triangle)
You must connect points on diagonale.
Then hypotenuse =
sqrt ( 105 ^ 2 + 88 ^ 2 ) =
sqrt ( 11025 + 7744 ) =
sqrt ( 18769 ) = 137 m
To find the length of the hypotenuse of each triangle, we can use the formula for the area of a triangle. Given that the rectangle measures 105 by 88 meters, the total area of the rectangle is:
A_rect = length * width = 105 * 88 = 9240 square meters.
Since the city council wants to divide the block into two triangles of equal area, each triangle will have an area equal to half of the rectangle's area, which is:
A_triangle = A_rect / 2 = 9240 / 2 = 4620 square meters.
Now, let's find the length of the base of the triangle. The base of the triangle will be the same as the width of the rectangle, which is 88 meters.
Using the formula for the area of a triangle:
A_triangle = (base * height) / 2,
we can rearrange the formula to solve for the height:
height = (2 * A_triangle) / base.
Substituting the known values:
height = (2 * 4620) / 88 = 105 meters.
Now that we know the base and height of the triangle, we can use the Pythagorean theorem to find the length of the hypotenuse, which is the square root of the sum of the squares of the base and height:
hypotenuse = √(base^2 + height^2)
= √(88^2 + 105^2)
≈ √(7744 + 11025)
≈ √(18769)
≈ 137 meters.
Therefore, the length of the hypotenuse of each triangular area is approximately 137 meters.