Question

a new bridge structure requires triangles that are in a ratio of 1:1. if ac = 5x - 5 and ec = 3x + 9, find the distance between the top and

Explanation:

Step1: Set up the equation

Since the triangles are in a 1:1 ratio, $AC = EC$. So we set up the equation $5x - 5=3x + 9$.

Step2: Solve for x

Subtract $3x$ from both sides: $5x-3x - 5=3x-3x + 9$, which simplifies to $2x-5 = 9$. Then add 5 to both sides: $2x-5 + 5=9 + 5$, giving $2x=14$. Divide both sides by 2: $x = 7$.

Step3: Find the length

Substitute $x = 7$ into the expression for $AC$ (we could also use $EC$). $AC=5x - 5=5\times7-5=35 - 5=30$.

Answer:

30