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Charlie runs a screen printing company and is resetting a machine he uses to print triangular banners. He knows the amount of material he needs for the banner as well as the height of the triangle, but he needs to set the machine to a new measurement for the triangle's base.

To help Charlie determine the new measurement, rewrite the standard formula for the area of a triangle, [tex]A=\frac{1}{2}bh[/tex], to solve for the base, [tex]b[/tex].

Enter the correct answer in the box.

[tex]b=[/tex]



Answer :

GinnyAnswer
Certainly! Let's start with the standard formula for the area of a triangle:

[tex]\[ A = \frac{1}{2} b h \][/tex]

where:
- [tex]\( A \)[/tex] is the area of the triangle,
- [tex]\( b \)[/tex] is the base of the triangle,
- [tex]\( h \)[/tex] is the height of the triangle.

We need to solve this formula for the base [tex]\( b \)[/tex]. Here's the step-by-step process to isolate [tex]\( b \)[/tex]:

1. Start with the given formula:
[tex]\[ A = \frac{1}{2} b h \][/tex]

2. Eliminate the fraction by multiplying both sides of the equation by 2:
[tex]\[ 2A = b h \][/tex]

3. Solve for [tex]\( b \)[/tex] by dividing both sides of the equation by [tex]\( h \)[/tex]:
[tex]\[ b = \frac{2A}{h} \][/tex]

So, 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]

Thus, Charlie can set the machine to a new measurement for the triangle's base using this formula.