Question

ΔABC is similar to ΔAXY by a ratio of 4:3. If BC = 24, what is the length of XY? triangles ABC and AXY that share vertex A where point X is between points A and B and point Y is between points A and C XY = 18 XY = 32 XY = 6 XY = 8

Answer 1

Answer:

$XY = 18$

Step-by-step explanation:

Given

$ABC:AXY = 4 : 3$

$BC = 24$

Required

Find XY

Represent BC and XY as a ratio;

$BC : XY = 24 : xy$

Recall that:

$ABC:AXY = 4 : 3$

Equate both ratios;

$24 : xy = 4 : 3$

Convert to fractions

$\frac{24}{xy} = \frac{4}{3}$

Cross Multiply

$xy * 4 = 24 * 3$

$xy * 4 = 72$

Divide through by 3

$xy * 4/4 = 72/4$

$xy = 18$

Hence:

$XY = 18$