Answer:
• Altitude = 8 inches
,
• Side = 31 inches
Step-by-step explanation:
Let the altitude to the given side = x inches
One side of the triangle is 7 inches more than 3 times the length of the altitude.
• Length of the side = (3x+7) inches
,
• The area if the triangle = 124 square inches
If the altitude is to the given side, then the given side is the base of the triangle.

We then solve for x:

Since the equation is quadratic, we solve it using the quadratic formula:
![\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\; where\; a=3,b=7,c=-248 \\ =\frac{-7\pm\sqrt[]{7^2-4(3)(-248)}}{2*3}=\frac{-7\pm\sqrt[]{49-(-2976)}}{6} \\ =\frac{-7\pm\sqrt[]{49+2976}}{6}=\frac{-7\pm\sqrt[]{3025}}{6} \\ =(-7\pm55)/(6) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/xss191robn23xaercio3wm4tqm4rqvis91.png)
Therefore, the values of x are:

Thus, we have that:
• Length of the altitude = 8 inches
,
• Length of the side = (3x+7)=3(8)+7=31 inches
CHECK
