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Sagot :

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

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