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?
Well, with the bases of the rectangle and triangle doubled, we'll have a super-sized building! But fear not, my friend, the force of the wind against the side of the building won't be too bothered. You see, wind is a playful force and enjoys a good challenge. Just like blowing on a bigger slice of pizza, the wind will simply exert more force on the larger surface area. So, while the building might feel a bit of a breeze, it should still be able to handle it with style!
When the bases of the rectangle and triangle in the building above are doubled to 40 ft, while keeping the height the same, the area of both figures will increase.
Let's consider the rectangle first. The area of a rectangle is given by the formula: Area = Length × Width. Since the width is doubled, the new area of the rectangle will be double the original area. This means that the force of the wind against the side of the building will also double.
Now, let's consider the triangle. The area of a triangle is given by the formula: Area = (Base × Height) / 2. Since only the base is doubled and the height remains the same, the new area of the triangle will be double the original area. Again, this means that the force of the wind against the side of the building will double.
In conclusion, if the bases of the rectangle and triangle in the building are doubled while the height remains the same, the force of the wind against the side of the building will double for both figures.
To determine how the force of the wind against the side of the building is affected, we need to consider the area of each figure. The force of the wind depends on the area that comes into contact with it.
Let's break down the problem step by step:
1. Start by calculating the original areas of the rectangle and triangle.
- Original base of the rectangle = X ft
- Original height of the rectangle = Y ft
- Original area of the rectangle = X * Y
- Original base of the triangle = X ft (same as the rectangle's base)
- Original height of the triangle = Z ft
- Original area of the triangle = (X * Z)/2
2. Now, suppose the bases of the rectangle and triangle are doubled to 40 ft, while the height of each figure remains the same.
- New base of the rectangle = 40 ft
- New base of the triangle = 40 ft
3. Calculate the new areas of the rectangle and triangle using the new base measurements.
- New height of the rectangle = Y ft (remains the same)
- New area of the rectangle = (40 ft) * Y
- New height of the triangle = Z ft (remains the same)
- New area of the triangle = (40 ft * Z)/2
4. Compare the original and new areas of the rectangle and triangle.
- The ratio of the new rectangle area to the original rectangle area is (40 ft) / X.
- The ratio of the new triangle area to the original triangle area is [(40 ft * Z)/2] / [(X * Z)/2] = (40 ft) / X.
In conclusion, when the bases of the rectangle and triangle are doubled while the height remains the same, the areas of both shapes increase in direct proportion to the increase in base length. Therefore, the force of the wind against the side of the building will also increase in direct proportion to the increase in base length.