Question

find the perimeter of the triangle. round your answer to the nearest hundredth.

Explanation:

1. First, assume the coordinates of the vertices of the triangle. Let's say the coordinates of \(W=(x_1,y_1)\), \(X=(x_2,y_2)\), and \(Y=(x_3,y_3)\).

• Since the grid - based graph is not provided with exact coordinates, for the sake of illustration, if \(W=(1,1)\), \(X=(4,4)\), and \(Y=(4,1)\).
• Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) to find the lengths of the sides of the triangle.

1. Calculate the length of side \(WX\):

• For points \(W=(x_1,y_1)=(1,1)\) and \(X=(x_2,y_2)=(4,4)\), we have \(d_{WX}=\sqrt{(4 - 1)^2+(4 - 1)^2}=\sqrt{3^2+3^2}=\sqrt{9 + 9}=\sqrt{18}\approx4.24\).

1. Calculate the length of side \(XY\):

• For points \(X=(x_1,y_1)=(4,4)\) and \(Y=(x_2,y_2)=(4,1)\), we have \(d_{XY}=\sqrt{(4 - 4)^2+(1 - 4)^2}=\sqrt{0+( - 3)^2}=\sqrt{9}=3\).

1. Calculate the length of side \(YW\):

• For points \(Y=(x_1,y_1)=(4,1)\) and \(W=(x_2,y_2)=(1,1)\), we have \(d_{YW}=\sqrt{(1 - 4)^2+(1 - 1)^2}=\sqrt{( - 3)^2+0}=\sqrt{9}=3\).

1. Calculate the perimeter \(P\) of the triangle:

• \(P=d_{WX}+d_{XY}+d_{YW}\approx4.24 + 3+3=10.24\).

Step1: Assume coordinates

Assume \(W=(1,1)\), \(X=(4,4)\), \(Y=(4,1)\)

Step2: Calculate \(WX\) length

Use distance formula \(d_{WX}=\sqrt{(4 - 1)^2+(4 - 1)^2}=\sqrt{18}\approx4.24\)

Step3: Calculate \(XY\) length

Use distance formula \(d_{XY}=\sqrt{(4 - 4)^2+(1 - 4)^2}=3\)

Step4: Calculate \(YW\) length

Use distance formula \(d_{YW}=\sqrt{(1 - 4)^2+(1 - 1)^2}=3\)

Step5: Calculate perimeter

\(P = 4.24+3 + 3=10.24\)

Answer:

10.24