Question

18 use the image below to solve for x using your knowledge of parallel lines and similar triangles. 6 15 x 14 x = units

Explanation:

Step1: Apply similar - triangles property

If two lines are parallel, the two triangles are similar. The ratios of corresponding sides of similar triangles are equal. Let the smaller triangle have sides 6 and the side parallel to the base, and the larger triangle have sides \(6 + 15=21\) and 14. The ratio of the sides of the two similar triangles gives the equation \(\frac{6}{6 + 15}=\frac{x}{14}\).

Step2: Cross - multiply and solve for x

Cross - multiplying the equation \(\frac{6}{21}=\frac{x}{14}\) gives \(21x=6\times14\). Then \(21x = 84\), and \(x=\frac{84}{21}\).

Step3: Calculate the value of x

\(x = 4\)

Answer:

4