Question

Find the perimeter of the image below:

25.8 units

26.1units

27.5 units

28.6 units

Answer 1

Start by calculating the length of each side by distance formula:

`d = \sqrt{( ({y2 - y1})^(2)+ ( {x2 - x1})^(2)} )`

`qr =\sqrt{(({y2 - y1})^(2)+({x2 - x1})^(2)} ) \\ \sqrt{( ({5 - 0})^(2) + ( {4 - 2})^(2)} ) \\ = \sqrt{{5}^(2) + {2}^(2)} = √(25 + 4) = √(29)`

`rs =\sqrt{(({y2 - y1})^(2)+({x2 - x1})^(2)} ) \\ =\sqrt{(({7 - 5})^(2)+({8 - 4})^(2)} ) \\ = \sqrt{ {2}^(2) + {4}^(2)} = √(4 + 16) = √(20) \\ √(4) \: * √(5) = 2 √(5)`

`st =\sqrt{(({y2 - y1})^(2)+({x2 - x1})^(2)} ) \\=\sqrt{(({4 - 7})^(2)+({6 - 8})^(2)} ) \\=\sqrt{(({ - 3})^(2)+({ - 2})^(2)} ) = √(9 + 4) \\ = √(13)`

`tu =\sqrt{(({y2 - y1})^(2)+({x2 - x1})^(2)} ) \\qr =\sqrt{(({3 - 4})^(2)+({10 - 6})^(2)} ) \\ \sqrt{( {( - 1)}^(2) + {(4)}^(2) )} = √(1 + 16) \\ = √(17)`

`uq =\sqrt{(({y2 - y1})^(2)+({x2 - x1})^(2)} ) \\ =\sqrt{(({0 - 3})^(2)+({2 - 10})^(2)} ) \\ = \sqrt{ {( - 3)}^(2) + {( - 8)}^(2) } = √(9 + 64) \\ = √(73)`
Now we add up all 5 side lengths to find the perimeter: P = QR + RS + ST + TU + UQ

`p = √(29) + 2 √(5) + √(13) + √(17) \\ + √(73) \\ = 5.39 + 4.47 + 3.61 + 4.12 \\ + \: 8.54 = 26.13 \: units`
Therefore B) 26.1 units is the closest answer