Step 1:
Write the formula for the area of a triangle
[tex]\text{Area of a triangle = }\frac{Base\text{ }\times\text{ Height}}{2}[/tex]Step 2:
Given data
Let the base = m
height = 2m - 4
Step 3:
Substitute in the formula
[tex]\begin{gathered} \text{Area = }\frac{Base\text{ }\times\text{ Height}}{2} \\ 15\text{ = }\frac{m(2m\text{ - 4)}}{2} \\ \text{Cross multiply} \\ m(2m\text{ - 4) = 2}\times15 \\ 2m^2\text{ - 4m = 30} \\ \text{Divide both sides of the equation by 2} \\ m^2\text{ - 2m - 15 = 0} \end{gathered}[/tex]Step 4
Factorize the equation to find m.
[tex]\begin{gathered} m^2\text{ - 2m - 15 = 0} \\ m^2\text{ -5m + 3m - 15 = 0} \\ m(m\text{ - 5) + 3(m - 5) = 0} \\ (m\text{ + 3)(m - 5) = 0} \\ m\text{ = -3 or 5} \end{gathered}[/tex]m = 5, the value of m cannot be negative because the measurement of length cannot be negative.
Final answer
Base = 5 inches
Height = 2(5 ) - 4 = 10 - 4 = 6 inches
Base = 5 inches
Height = 6 inches
