Question

find the approximate perimeter of rectangle abcd plotted below. a(-6,0) b(4,5) c(8,-3) d(-2,-8) choose 1 answer: a 39.0 b 40.2 c 41.4 d 42.6

Explanation:

Step1: Use distance formula for side AB

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $A(-6,0)$ and $B(4,5)$, we have $x_1=-6,y_1 = 0,x_2=4,y_2 = 5$. Then $AB=\sqrt{(4 + 6)^2+(5 - 0)^2}=\sqrt{100 + 25}=\sqrt{125}\approx11.18$.

Step2: Use distance formula for side BC

For points $B(4,5)$ and $C(8,-3)$, $x_1 = 4,y_1=5,x_2 = 8,y_2=-3$. Then $BC=\sqrt{(8 - 4)^2+(-3 - 5)^2}=\sqrt{16 + 64}=\sqrt{80}\approx8.94$.

Step3: Calculate the perimeter of rectangle

The perimeter of a rectangle $P = 2(AB + BC)$. Substitute the values of $AB$ and $BC$: $P=2(11.18+8.94)=2\times20.12 = 40.24\approx40.2$.

Answer:

B. 40.2