Let's label the sides of the triangle out from the given information.
As we can see above, we labeled the distance from the top of the leg to the support bar as "x".
Since the legs are 86 inches long, then we can say that from the support bar to the bottom of the leg would be "86 - x".
Since the support bar is parallel to the ground, then based on theorem, we can say that ∆ABC and ∆DBE are similar triangles.
By similarity theorem, we can say that the ratios of the corresponding sides of both triangles are equal.
[tex]\frac{BD}{AB}=\frac{DE}{AC}[/tex][tex]\frac{x}{86}=\frac{28}{58}[/tex]
From this, we can now solve for x. The steps are shown below.
1. Cross-multiply both sides of the equation.
[tex](x)(58)=(28)(86)[/tex][tex]58x=2408[/tex]
2. Divide both sides of the equation by 58.
[tex]\frac{58x}{58}=\frac{2408}{58}[/tex][tex]x=41.517\approx42in[/tex]
The value of x is approximately 42 inches.
Hence, Lauren should attach the horizontal support bar 42 inches from the top of the legs.
