Question

i \can\ similarity if efgh ~ jklm. what is the value of x? (diagrams of two similar quadrilaterals, efgh with sides x (fe) and 2x + 1.5 (gh), jklm with sides 8 (kj), 7 (kl), 15 (jm), 18 (ml)) a 8 b 4 c 6 d 5 13 a

Explanation:

Step1: Use the property of similar polygons

For similar polygons \(EFGH\sim JKLM\), the ratios of corresponding sides are equal.
We can set up the proportion \(\frac{x}{8}=\frac{2x + 1.5}{17}\) (since \(15+ 2=17\) and \(18 - 1=17\)). Cross - multiply gives \(17x=8(2x + 1.5)\).

Step2: Expand and solve the equation

Expand \(8(2x + 1.5)\) to get \(16x+12\). So the equation becomes \(17x=16x + 12\).
Subtract \(16x\) from both sides: \(17x-16x=16x + 12-16x\), which simplifies to \(x = 6\).

Answer:

C. 6