Question

What is AC? A √162 = 12.7 B√98 = 9.9 C√117 ≈ 10.8 D√72 = 8.5

Answer 1

The most appropriate choice for distance formula will be given by Length of AC = $\sqrt{72} = 8.5 units$

What is distance?
Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in everyday language (e.g. "two counties over").

What is distance formula?

Distance formula is used to find the distance between two points.

Let A and B be two points with coordinate $(x_1, y_1)$  and $(x_2, y_2)$ respectively

Distance between A and B = $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2$

Here,

Coordinate of A = (1, 1)

Coordinate of E = (4, 4)

Coordinate of C = (7, 7)

Length of AE =

$\sqrt{(4-1)^2 + (4-1)^2}\\\sqrt{9 + 9}\\\sqrt{18}\\3\sqrt{2} units$

Length of EC =

$\sqrt{(7-4)^2 + (7-4)^2}\\\sqrt{9 + 9}\\\sqrt{18}\\3\sqrt{2} units$

Length of AC = Length of AE + Length of EC

= $3\sqrt{2} + 3\sqrt{2} = 6\sqrt{2} units$ =$\sqrt{72} units = 8.5 units$

Fourth option is correct

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