Here, we have two pairs of similar triangles.
Let's find the values of x and y.
• Sol,vin,g for x:
Given:
Length of longer base = 9
Length of shorter base = 5
Length of smaller leg = 8
Let's solve for x.
Since the triangles are similar, the corresponding sides will be in proportion.
To solve for x, apply the proportionality equation:
[tex]\frac{9}{x}=\frac{6}{8}[/tex]
Cross multiply and solve for x:
[tex]\begin{gathered} 6x=9*8 \\ \\ 6x=72 \\ \\ \text{ Divide both sides by 6:} \\ \frac{6x}{6}=\frac{72}{6} \\ \\ x=12 \end{gathered}[/tex]
• Solving for y:
Given:
Length of longer base = 3
Length of longer leg = 6
Length of smaller leg = 4
Length of total base = y
To solve for y, we have the equation:
[tex]\frac{6}{3}=\frac{4}{y-3}[/tex]
Cross multiply and solve for y:
[tex]\begin{gathered} 6(y-3)=4*3 \\ \\ 6y-6(3)=12 \\ \\ 6y-18=12 \\ \\ \text{ Add 18 to both sides:} \\ 6y-18+18=12+18 \\ \\ 6y=30 \\ \\ \text{ Divide both sides by 6:} \\ \frac{6y}{6}=\frac{30}{6} \\ \\ y=5 \end{gathered}[/tex]
ANSWER:
• x = 12
• y = 5
