Question

If DGH ~ DEF, find the value of x.

Answer 1

x = 25

Explanation:

DGH is congruent with DEF

(meaning DG is congruent with DE, GH is congruent with EF, DH is congruent with DF)

DG = 52 & DE = 91

GH = x + 3 & EF = 2x-1

in this case we can disregard DH and DF since its providing no information

write the equation as:

52 x+3

---- = -----

91 2x-1

cross multiply 52 and 2x-1 then cross multiply 91 and x+3

this should give you:

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

distribute:

104x - 52 = 91x + 273

then solve using algebra

13x - 52 = 263

13 = 325

x = 25

Hope this helps!!

Answer 2

Given the similarity of triangles DGH and DEF, the corresponding sides ratio
`\((DG)/(DE) = (GH)/(EF)\)` is established. Solving, x = 25, confirming the value for the given problem.

We have been given that DGH ~ DEF

According to the similarity of triangles, the ratio of corresponding sides is proportional:

`\[(DG)/(DE) = (GH)/(EF)\]`

Substitute the given values:

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

Cross-multiply:

`\[(2x - 1) \cdot 52 = (x + 3) \cdot 91\]`

Expand:

104x - 52 = 91x + 273

Combine like terms:

104x - 91x = 273 + 52

Simplify:

13x = 325

Divide by 13:

x = 25

Therefore, the value of x is 25.