Question

Please help me with the two questions!

Answer 1

`3)\ x = 8`

`4)\ x = 12`

Explanation:

Given

The similar triangles

Required

Solve for x

TUV to TLM implies that, the corresponding sides are:

`TU \to TL`

`TV \to TM`

`UV \to LM`

To solve for x, we use the following equivalent ratios

`TV : TM =TU:TL`

This gives:

`24 : x + 8=36 : 24`

Express as fraction

`(24 )/( x + 8) =(36 )/( 24)`

Cross Multiply

`36(x + 8) =576`

Divide both sides by 36

`x + 8 =16`

Subtract 8 from both sides

`x = 8`

FGH to WVU implies that, the corresponding sides are:

`FG \to WV`

`FH \to WU`

`GH \to VU`

To solve for x, we use the following equivalent ratios

`FH : WU =FG:WV`

This gives:

`x + 3 : 5 = 27 : 9`

Express as fraction

`(x + 3 )/( 5 )= (27 )/( 9)`

`(x + 3 )/( 5 )= 3`

Cross Multiply

`x + 3 = 3 * 5`

`x + 3 = 15`

Subtract 3 from both sides

`x = 12`