suppose the bases of the rectangle and triangle in the building above are doubled to 40ft,but the height of each figure remains the same.How is the force of the wind against the side of the building affected?
To determine how the force of the wind against the side of the building is affected, we need to consider the surface area of each shape.
1. Rectangle:
The surface area of a rectangle is given by the formula A = base x height. If the base of the rectangle is doubled to 40ft, but the height remains the same, then the new surface area of the rectangle is 40ft x height.
2. Triangle:
The surface area of a triangle is given by the formula A = (base x height) / 2. If the base of the triangle is doubled to 40ft, but the height remains the same, then the new surface area of the triangle is (40ft x height) / 2.
Now, in order to determine how the force of the wind is affected, we need to compare the original surface area of each shape with the new surface area.
Let's assume the original surface area of the rectangle was AR, and the original surface area of the triangle was AT.
Comparing the new and original surface areas of each shape:
1. Rectangle: New surface area (NR) = 40ft x height, Original surface area (OR) = base x height = BR x height
The ratio of the new surface area to the original surface area of the rectangle can be calculated as NR / OR = (40ft x height) / (BR x height) = 40ft / BR.
2. Triangle: New surface area (NT) = (40ft x height) / 2, Original surface area (OT) = (base x height) / 2 = BT x height / 2
The ratio of the new surface area to the original surface area of the triangle can be calculated as NT / OT = [(40ft x height) / 2] / [(BT x height) / 2] = 40ft / BT.
The force of the wind against the side of the building is affected by the surface area of the shapes. Therefore, if the bases of the rectangle and triangle are doubled to 40ft, but the height remains the same, the force of the wind against the side of the building will increase because the surface area of both the rectangle and triangle has increased by a factor of 40ft/BR and 40ft/BT respectively.