Question

4 cm

A
C
If BX = 2 cm, XA = 3 cm, and BY = 3, find the value of YC.
O 5.5 cm
5 cm
B
O 45 cm
Y
4

Answer 1

Explanation:

Comment and answer

ABC is similar to XBY The triangles are similar because

• B is a common angle to both
• <A = <BXY AB is a transversal cutting 2 parallel lines
• <C = <BYX BC is a transversal cutting 2 parallel lines

BX = 2 Given

XA = 3 Given

BY = 3 Given

YC = x Object of question

BX/(BX + XA) = BY / (BY + YC) Parts of two similar triangles

2/(2 + 3) = 3/(3+ x) Combine the left

2/5 = 3/(3 + x) Cross Multiply

2*(3 + x) = 3*5 Remove the brackets

6 + 2x = 15 Subtract 6 from both sides

6-6+2x = 15 - 6 Combine

2x = 9 Divide by 2

2x/2 = 9/2

x = 4.5

Answer

x = 4.5 or D