Sure, let's work through the steps to solve for the base [tex]\( b \)[/tex] in the formula for the area of a triangle.
The standard formula for the area of a triangle is given by:
[tex]\[ A = \frac{1}{2} b h \][/tex]
where [tex]\( A \)[/tex] is the area, [tex]\( b \)[/tex] is the base, and [tex]\( h \)[/tex] is the height of the triangle.
To solve for [tex]\( b \)[/tex], follow these steps:
1. Start with the equation:
[tex]\[ A = \frac{1}{2} b h \][/tex]
2. To eliminate the fraction, multiply both sides of the equation by 2:
[tex]\[ 2A = b h \][/tex]
3. Now, to isolate [tex]\( b \)[/tex], divide both sides of the equation by [tex]\( h \)[/tex]:
[tex]\[ b = \frac{2A}{h} \][/tex]
So, the formula for the base [tex]\( b \)[/tex] in terms of the area [tex]\( A \)[/tex] and the height [tex]\( h \)[/tex] is:
[tex]\[ b = \frac{2A}{h} \][/tex]
Hence, the new measurement for the base that Charlie needs is:
[tex]\[ b = \frac{2A}{h} \][/tex]
