Answer:
[tex]x = 10[/tex]
Step-by-step explanation:
Given
[tex]AB = 8[/tex]
[tex]AC = x[/tex]
[tex]QR = 12[/tex]
[tex]QS = 15[/tex]
Required
Find x
Because both triangles are similar, we have:
[tex]AB : AC = QR : QS[/tex] --- Equivalent ratios
This gives:
[tex]8 : x = 12 : 15[/tex]
Convert to fraction
[tex]\frac{8}{x} = \frac{12}{15}[/tex]
Cross Multiply:
[tex]12 * x = 8* 15[/tex]
[tex]12x = 120[/tex]
Divide both sides by 12
[tex]x = \frac{120}{12}[/tex]
[tex]x = 10[/tex]
