Question

Triangle XZW ~ triangle XYV, find the perimeter of triangle XZW

Answer 1

176.4

Step-by-step explanation

as the triangle are similar we can set a proportion

Step 1

find the YZ value

a) let

`ratio1=\frac{hypotenuse}{rigth\text{ side}}`

so,for triangle XZW

`ratio=(40+32)/(28+YZ)`

and for triangle XYV

`ratio=(40)/(28)`

as the ratios are equal, we can set a proportion

`(40+32)/(28+YZ)=(40)/(28)`

b) now,solve for YZ

`\begin{gathered} (40+32)/(28+YZ)=(40)/(28) \\ (72)/(28+YZ)=(40)/(28) \\ cross\text{ multiply} \\ 72*28=40(28+YZ) \\ 2016=1120+40YZ \\ subtract\text{ 1120 in both sides} \\ 2016-1120=1120+40YZ-1120 \\ 896=40YZ \\ divide\text{ bothsides by 40} \\ (896)/(40)=(40YZ)/(40) \\ 22.4=YZ \end{gathered}`

so

YZ=22.4

Step 2

find the length of the side WZ

a) let

`ratio=\frac{hypotenuse\text{ }}{base}`

hence

`\begin{gathered} ratio_1=(40+32)/(WZ)=(72)/(WZ) \\ ratio_2=(40)/(30) \end{gathered}`

set the proportion and solve for YZ

`\begin{gathered} ratio_1=\text{ ratio}_2 \\ (72)/(WZ)=(40)/(30) \\ cross\text{ multiply} \\ 72*30=40WZ \\ 2160=40WZ \\ divide\text{ both sides by 40} \\ (2160)/(40)=(40WZ)/(40) \\ 54=WZ \end{gathered}`

Step 3

finally, find the perimeter of triangle XZW

Perimeter is the distance around the edge of a shape,so

`Perimeter_(\Delta XZW)=XY+YZ+ZW+WV+VX`

replace and calculate

`\begin{gathered} Per\imaginaryI meter_(\Delta XZW)=XY+YZ+ZW+WV+VX \\ Perimeter_(\Delta XZW)=28+22.4+54+32+40 \\ Perimeter_(\Delta XZW)=176.4 \end{gathered}`

therefore, the answer is

176.4

I hope this helps you