Question

Find the missing length of the following trapezoid

Answer 1

Answer:

1) The length of $DC$ is 20.

2) The length of $PS$ is 17.

Step-by-step explanation:

1) If $DR = RE$ and $CS = SB$, then we can use the following proportionality ratio:

$\frac{DE}{DR} = \frac{32 - x}{26 - x}$ (1)

Where $x$ is the length of segment $\overline{CD}$.

If $DE = 2\cdot DR$, then the value of $x$ is:

$2 = \frac{32-x}{26-x}$

$52 - 2\cdot x = 32 - x$

$20 = x$

The length of $DC$ is 20.

2) If $QV = VP$ and $RW = WS$, then we can use the following proportionality ratio:

$\frac{QP}{QV} = \frac{x-7}{12-7}$ (2)

Where $x$ is the length of segment $\overline{PS}$.

If $QP = 2\cdot QV$, then the value of $x$ is:

$2 = \frac{x-7}{5}$

$10 = x-7$

$x = 17$

The length of $PS$ is 17.