Answer:
48 square feet
Step-by-step explanation:
Given
Before expansion
[tex]A_1 = \frac{1}{2}bh[/tex] --- area of a triangle
[tex]A_1 = 16ft^2[/tex] --- value of the area
After the base and height were expanded, the area becomes:
[tex]A_2 = \frac{1}{2}BH[/tex]
Where
[tex]B = 2b[/tex]
[tex]H = 2h[/tex]
Substitute 2b for B and 2h for H in [tex]A_2 = \frac{1}{2}BH[/tex]
[tex]A_2 = \frac{1}{2} * 2b * 2h[/tex]
[tex]A_2 = \frac{1}{2} * 2*2*b*h[/tex]
[tex]A_2 = \frac{1}{2} * 4*b*h[/tex]
Rewrite as:
[tex]A_2 = 4 * \frac{1}{2} *b*h[/tex]
[tex]A_2 = 4 * \frac{1}{2}bh[/tex]
Recall that: [tex]A_1 = \frac{1}{2}bh[/tex]
So, we have:
[tex]A_2 = 4 * A_1[/tex]
Substitute 16 for [tex]A_1[/tex]
[tex]A_2 = 4 * 16[/tex]
[tex]A_2 = 64[/tex]
So, the area is [tex]64ft^2[/tex] after the dimensions were expanded
The area increased by:
[tex]Increment = A_2 - A_1[/tex]
[tex]Increment = 64 - 16[/tex]
[tex]Increment = 48[/tex]
It increased by [tex]48ft^2[/tex]
