Find the perimeter of the image below: 37 units, 38 units, 39 units, 40 units

Solution:

Given, P(-2, 11) Q(-4, 5) R(2, 0) S(1, 7) T(8, 7)

We have to find the perimeter of the given figure.

\(distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)

Now, \(PQ=\sqrt{(-4-(-2))^{2}+(5-11)^{2}}=\sqrt{(-2)^{2}+(-6)^{2}}=\sqrt{4+36}=\sqrt{40}\)=6.32

\(QR=\sqrt{(-4-2)^{2}+(5-0)^{2}}=\sqrt{(-6)^{2}+(5)^{2}}=\sqrt{36+25}=\sqrt{61}\)=7.81

\(RS=\sqrt{(1-2)^{2}+(0-7)^{2}}=\sqrt{(-1)^{2}+(-7)^{2}}=\sqrt{1+49}=\sqrt{50}\)=7.07

\(ST=\sqrt{(8-1)^{2}+(7-7)^{2}}=\sqrt{(49)^{2}+(0)^{2}}=\sqrt{49+0}=\sqrt{49}=7\)

\(TP=\sqrt{(-2-8)^{2}+(11-7)^{2}}=\sqrt{(-10)^{2}+(4)^{2}}=\sqrt{100+16}=\sqrt{116}=10.77\)

Perimeter = PQ + QR + RS + ST + TP

Perimeter = 6.32 + 7.81 + 7.07 + 7 + 10.77

= 38.97 units.

Therefore, the perimeter is 38.97 units.

Summary:

The perimeter of the image is 38.97 units.

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