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The ABC Toy Company is creating two similar pieces for a board game, as shown below. Find the value of y that makes the two pieces similar. Triangle GHI is shown with sides GH marked as 4, GI marked as 6, and HI marked as x. Triangle JKL is shown with sides JK marked as 8, JL marked as y, and KL marked as z. Numerical Answers Expected! Answer for Blank 1:

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MrRoyalid

Answer:

[tex]y = 12[/tex]

Step-by-step explanation:

Given

Triangles GHI and JKL

See attachment for illustration

Required

Find the value of y

We have:

[tex]GH = 4[/tex]

[tex]GI = 6[/tex]

[tex]JK = 8[/tex]

[tex]JL = y[/tex]

Sides GH and JK are similar

Sides GI and KL are also similar

Since both triangles are similar, then the ratio of similar sides must be equal.

[tex]Ratio = GH : JK[/tex]

[tex]Ratio = GI : JL[/tex]

Equate both ratios

[tex]GH:JK = GI:JL[/tex]

Substitute values for GH, GI, JK and JL

[tex]4 : 8 = 6 : y[/tex]

Convert to fractions

[tex]\frac{4}{8} = \frac{6}{y}[/tex]

[tex]\frac{1}{2} = \frac{6}{y}[/tex]

Cross Multiply

[tex]1 * y = 6 * 2[/tex]

[tex]y = 12[/tex]

View image MrRoyal

Answer:

y = 12.

Step-by-step explanation:

I just took the test and got it right. This is because 8 is twice the size as 4, so it can be determined that all you need to do is multiply 6 by 2. I hope this helps!

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