Question

What is the value of x and the length of segment DE?

Answer 1

Answer:

$x = 6.6$ and $DE = 16.2$

Step-by-step explanation:

The question is incomplete as the attachment to solve segment DE is missing. However, see attached for complete question.

Given

$\frac{5}{9}= \frac{9}{(2x+3)}$

Required

Find x

Length of DE

To find x, we need to first simplify the given equation

$\frac{5}{9}= \frac{9}{(2x+3)}$

Multiply both sides by $9(2x+3)$

$\frac{5}{9} * 9(2x + 3) = \frac{9}{(2x+3)} * 9(2x + 3)$

$5(2x + 3) = 9(9)$

$10x + 15 = 81$

Subtract 15 from both sides

$10x + 15 - 15 = 81 - 15$

$10x = 66$

Divide both sides by 10

$\frac{10x}{10} = \frac{66}{10}$

$x = \frac{66}{10}$

$x = 6.6$

From the attached;

$DE = 2x + 3$

Substitute 6.6 for x

$DE = 2(6.6) + 3$

$DE = 13.2 + 3$

$DE = 16.2$

Hence $x = 6.6$ and $DE = 16.2$