Question

Point upper A is on line upper Y upper X. Point upper B is on diagonal upper Y upper Z. A small square box is marked in angle upper A and angle upper X.


If △XYZ ∼ △AYB
△
𝑋
𝑌
𝑍

∼

△
𝐴
𝑌
𝐵
, and YB=25
𝑌
𝐵
=
25
ft, YA=16
𝑌
𝐴
=
16
ft, and YZ = 88
𝑌
𝑍

=

88
ft, then what is the length of YX¯¯¯¯¯¯¯¯
𝑌
𝑋
¯
?

(1 point)
Responses

56.32 ft.
56.32 ft.

137.5 ft.
137.5 ft.

79 ft.
79 ft.

67.6 ft.

Answer 1

Since △XYZ ∼ △AYB with corresponding vertices X↔A, Y↔Y, Z↔B, the scale factor from the small to the large triangle is YZ/YB = 88/25. Then

YX = (88/25)·YA = (88/25)·16 = 1408/25 = 56.32 ft.

Answer: 56.32 ft.