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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

Respuesta :

MrRoyal

Answer:

[tex]XY = 18[/tex]

Step-by-step explanation:

Given

[tex]ABC:AXY = 4 : 3[/tex]

[tex]BC = 24[/tex]

Required

Find XY

Represent BC and XY as a ratio;

[tex]BC : XY = 24 : xy[/tex]

Recall that:

[tex]ABC:AXY = 4 : 3[/tex]

Equate both ratios;

[tex]24 : xy = 4 : 3[/tex]

Convert to fractions

[tex]\frac{24}{xy} = \frac{4}{3}[/tex]

Cross Multiply

[tex]xy * 4 = 24 * 3[/tex]

[tex]xy * 4 = 72[/tex]

Divide through by 3

[tex]xy * 4/4 = 72/4[/tex]

[tex]xy = 18[/tex]

Hence:

[tex]XY = 18[/tex]

Answer:

XY = 18

Step-by-step explanation:

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