Question

Given the picture, what is the length of AC? A) 4.5 B) 5 C) 7.5 D) 8

Answer 1

we know that

triangles BCD and ACE are similar

so, their ratios of sides must be equal

Calculation of y:

$\frac{BC}{AC}=\frac{CD}{CE}$

we can see that

AC=AB+BC

AC=y+3

CE=CD+DE

CE=4+6

CE=10

now, we can plug values

$\frac{3}{y+3}=\frac{4}{10}$

now, we can solve for y

$3*10=4*(y+3)$

$30=4y+12$

$30-12=4y+12-12$

$18=4y$

$y=4.5$

Calculation of AC:

we know that

AC=y+3

we can plug y

and we get

$AC=4.5+3$

$AC=7.5$...................Answer