Answer:
D) 45
Step-by-step explanation:
The distance formula tells you the distance between two points based on their coordinates. The distance (d) between points (x1, y1) and (x2, y2) is ...
d = √((x2-x1)^2 +(y2-y1)^2)
Working clockwise from the bottom, the two endpoints of the lower left side are (4, 5) and (1, 8). Then the distance between them is ...
d = √((1-4)^2 +(8-5)^2) = √((-3)^2 +3^2) = √(9+9) = √18
d = 3√2
Then the end points of the upper left side are (1, 8) and (14, 21). Its length is ...
d = √((14 -1)^2 +(21 -8)^2) = √(13^2 +13^2) = √338
d = 13√2
The other two sides of this rectangle are the same lengths, so the perimeter is ...
P = 3√2 + 13√2 + 3√2 + 13√2 = (3+13+3+13)√2 = 32√2 ≈ 45.255
P ≈ 45 . . . rounded to the nearest integer
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If you didn't already know it, this should help convince you that the length of the hypotenuse of an isosceles right triangle is √2 times the side length. Once you see that the lines have slopes of ±1, you know all you have to do is find the horizontal or vertical extent of the rectangle in the figure (16 units) and multiply that by √2 to get half the perimeter. The total perimeter is then 32√2.
Since you know that √2 ≈ 1.4, you know that none of the answers below 40 can possibly be correct.
