Question

XZW ~ XYV, find the perimeter of XZW.

Answer 1

Answer:

176.4

Step-by-step explanation:

We want perimeter of large triangle, so sum of all 3 sides:

XZ, ZW, and WX

Similar triangles have corresponding proportional sides. Thus looking at the 2 similar triangles, we can write:

$\frac{40}{28}=\frac{32+40}{28+YZ}$

Now, we solve for YZ:

$\frac{40}{28}=\frac{32+40}{28+YZ}\\\frac{40}{28}=\frac{72}{28+YZ}\\\frac{10}{7}=\frac{72}{28+YZ}\\10(28+YZ)=72*7\\280+10YZ=504\\10YZ=224\\YZ=22.4$

Now, XZ is 28 + 22.4 = 50.4

We can use same ratio to find ZW:

$\frac{40}{30}=\frac{72}{ZW}\\40ZW=30*72\\40ZW=2160\\ZW=54$

So the perimeter:

XZ + ZW + WX

50.4 + 54 + 72 = 176.4

Answer 2

The perimeter of a triangle is simply the sum of its three sides.

The perimeter of XZW  is 176.4 unit.

Given: ΔXZW ∼ ΔXTV

ΔXZW ∼ ΔXTV

So, all corresponding sides have the same ratio.

We can use same ratio to find ZW:

$\frac{40}{40+32} =\frac{30}{ZW}$

$\frac{40}{72} =\frac{30}{ZW} \\40ZW=72(30)\\ZW=\frac{2160}{40} \\ZW=54$

Now, we solve for YZ:

$\frac{30}{54} =\frac{28}{28+YZ} \\30(28+YZ)=28(54)\\28+YZ=\frac{1512}{30} \\YZ=50.4-28\\YZ=22.4$

So, $XZ=XY+YZ=28+22.4=50.4$

The perimeter of XZW

= XZ + ZW + WZ

= 50.4 + 54 + 72

= 176.4 unit.

Therefore, The perimeter of XZW  is 176.4 unit.

For more information:

https://brainly.com/question/21531254