Question

Using proportions to solve for missing sides.
DGH~DEF
Find the value of x.

Answer 1

25

Explanation:

If ΔDGH ~ ΔDEF , then
`(DG)/(DE)` =
`(GH)/(EF)`

`(x+3)/(2x-1)` =
`(52)/(91)`

After cross-multiplication: 52(2x - 1) = 91(x + 3)

104x - 52 = 91x + 273

13x = 325

x = 25

Answer 2

x = 25

Explanation:

DGH~DEF ⇒ their corresponding sides are proportional

then

`(DG)/(DE) =(GH)/(EF)`

then

`(52)/(91) =(x+3)/(2x-1)`

then

`(4)/(7) =(x+3)/(2x-1)`

then

4(2x-1) = 7(x+3) [cross multiply]

then

8x - 4 = 7x + 21

then

8x - 7x = 21 + 4

then

x = 25