If the length and width of a triangle are tripled, what is the effect on the area?
original area a = lw
(3w)(3l) = 9lw = 9a
To determine the effect on the area of a triangle when the length and width are tripled, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
Let's assume the original length of the triangle is 'l' and the original width is 'w'.
If the length and width are tripled, the new length would be 3l, and the new width would be 3w.
Now, let's calculate the original area of the triangle using the original length and width:
Original Area = (1/2) * l * w
Next, let's calculate the new area using the updated length and width:
New Area = (1/2) * (3l) * (3w)
Simplifying the expression, we get:
New Area = (1/2) * 9lw
New Area = 4.5 * (l * w)
From the calculations, we can see that if the length and width of a triangle are tripled, the area of the triangle will be multiplied by 4.5 or increased by a factor of 4.5.
To determine the effect of tripling the length and width of a triangle on its area, we need to understand the relationship between the dimensions of a triangle and its area.
The area of a triangle is calculated using the formula: A = (1/2) * b * h, where A represents the area, b represents the base (which can be considered the length of the triangle), and h represents the height (which can be considered the width of the triangle).
If we triple both the length (b) and width (h) of the triangle, the new dimensions will be 3b for the base and 3h for the height.
Substituting these new dimensions into the area formula, we get:
A = (1/2) * (3b) * (3h)
= (9/2) * b * h
Therefore, when the length and width of a triangle are tripled, the area of the triangle is multiplied by 9/2 or 4.5.
In other words, the area is increased by a factor of 4.5 when the length and width are tripled.