Answer :
Answer:
BD = 19
Step-by-step explanation:
given Δ BCD and Δ GEF are similar
Then the ratios of corresponding sides are in proportion
BC and GE are corresponding sides
BD and GF are corresponding sides
Then set up proportion and solve for x
[tex]\frac{BC}{GE}[/tex] = [tex]\frac{BD}{GF}[/tex] ← substitute values / expressions
[tex]\frac{x+4}{51}[/tex] = [tex]\frac{2x-7}{57}[/tex] ← cross multiply
51(2x - 7 ) = 57(x + 4 ) ← distribute parenthesis
102x - 357 = 57x + 228 ← subtract 57x from both sides
45x - 357 = 228 ← add 357 to both sides
45x = 585 ← divide both sides by 45
[tex]\frac{45x}{45}[/tex] = [tex]\frac{585}{45}[/tex]
x = 13
substitute x = 13 into the expression for BD
BD = 2x - 7 = 2(13 ) - 7 = 26 - 7 = 19
