Question

quadrilateral dcba is similar to quadrilateral abcd. determine the decimal value of x in quadrilateral abcd. > enter the answer in the space provided. use numbers instead of words. x =

Explanation:

Step1: Find the scale - factor

Since the two quadrilaterals are similar, we can find the scale - factor by comparing corresponding sides. Let's compare the sides $AB$ of the two quadrilaterals. The length of $AB$ in the larger quadrilateral is $17.5$ cm and in the smaller one is $2.5$ cm. The scale - factor $k=\frac{2.5}{17.5}=\frac{1}{7}$.

Step2: Use the scale - factor to find $x$

The side corresponding to $x$ in the larger quadrilateral has length $17.5$ cm. We know that $\frac{x}{17.5}=\frac{1}{7}$. Cross - multiplying gives $x=\frac{17.5}{7}$.

Step3: Calculate the value of $x$

$x = 2.5$

Answer:

$2.5$