Answer:
8 inches
Step-by-step explanation:
Use the formula for area of a triangle:
A = bh/2
"A" for area
"b" for base
"h" for height
What we know:
A = 34in²
h = 8 1/2 in
Substitute the known values into the formula
A = bh/2
(34in²) = b(8 1/2 in)/2
Isolate "b" to solve for the length of the base
(34in²) * 2 = b(8 1/2 in)/2 * 2 Multiply both sides by 2.
(68in²) = b(8 1/2 in)
(68in²)/(8 1/2 in) = b(8 1/2 in)/(8 1/2 in) Divide both sides by (8 2/1 in)
(68in²)/(8 1/2 in) = b Simplify and move variable to left
b = (68in²)/(8 1/2 in)
How to divide a mixed fraction:
[tex]b = \frac{68in^{2}}{8\frac{1}{2} in}[/tex]
[tex]b = \frac{68in^{2}}{\frac{17}{2} in}[/tex] Convert to improper fraction
[tex]b = 68in^{2} / \frac{17in}{2}[/tex] Reformat division
[tex]b = 68in^{2} * \frac{2}{17in}[/tex] Flip the second fraction
[tex]b = \frac{68in^{2} * 2}{17in}[/tex] Combine into numerator
[tex]b = 8in[/tex] Length of base
Therefore the base is 8 inches.
