Question

what is ae? enter your answer in the box. units

Explanation:

Step1: Assume similar - triangles property

If \(\triangle ABE\sim\triangle DCE\), then the ratios of corresponding sides are equal. So, \(\frac{AE}{DE}=\frac{BE}{CE}\). Also, we can use the property of parallel - lines in a triangle to set up an equation. Since the lines are parallel, we have \(\frac{AE}{DE}=\frac{AB}{CD}\). Substituting the given values: \(\frac{2x + 10}{x+3}=\frac{10}{4}\).

Step2: Cross - multiply the equation

Cross - multiplying the equation \(\frac{2x + 10}{x + 3}=\frac{10}{4}\) gives us \(4(2x + 10)=10(x + 3)\).
Expand both sides: \(8x+40 = 10x+30\).

Step3: Solve for \(x\)

Subtract \(8x\) from both sides: \(40=10x + 30-8x\), which simplifies to \(40 = 2x+30\).
Subtract 30 from both sides: \(2x=40 - 30=10\).
Divide both sides by 2: \(x = 5\).

Step4: Find the length of \(AE\)

Substitute \(x = 5\) into the expression for \(AE\). Since \(AE=2x + 10\), then \(AE=2\times5+10\).
\(AE=10 + 10=20\).

Answer:

20