Answer:
[tex]3)\ x = 8[/tex]
[tex]4)\ x = 12[/tex]
Step-by-step explanation:
Given
The similar triangles
Required
Solve for x
TUV to TLM implies that, the corresponding sides are:
[tex]TU \to TL[/tex]
[tex]TV \to TM[/tex]
[tex]UV \to LM[/tex]
To solve for x, we use the following equivalent ratios
[tex]TV : TM =TU:TL[/tex]
This gives:
[tex]24 : x + 8=36 : 24[/tex]
Express as fraction
[tex]\frac{24 }{ x + 8} =\frac{36 }{ 24}[/tex]
Cross Multiply
[tex]36(x + 8) =576[/tex]
Divide both sides by 36
[tex]x + 8 =16[/tex]
Subtract 8 from both sides
[tex]x = 8[/tex]
FGH to WVU implies that, the corresponding sides are:
[tex]FG \to WV[/tex]
[tex]FH \to WU[/tex]
[tex]GH \to VU[/tex]
To solve for x, we use the following equivalent ratios
[tex]FH : WU =FG:WV[/tex]
This gives:
[tex]x + 3 : 5 = 27 : 9[/tex]
Express as fraction
[tex]\frac{x + 3 }{ 5 }= \frac{27 }{ 9}[/tex]
[tex]\frac{x + 3 }{ 5 }= 3[/tex]
Cross Multiply
[tex]x + 3 = 3 * 5[/tex]
[tex]x + 3 = 15[/tex]
Subtract 3 from both sides
[tex]x = 12[/tex]
