Question

playground lukas is walking around the edge of the playground shown. how far will lukas have walked when he finishes one loop around the playground? round to the nearest unit, if necessary.
a(2,7) b(2,15) c(17,7)

Explanation:

Step1: Calculate length of AB

Use distance formula for points with same x - coordinate. $AB=\vert y_B - y_A\vert=\vert15 - 7\vert = 8$.

Step2: Calculate length of AC

Use distance formula for points with same y - coordinate. $AC=\vert x_C - x_A\vert=\vert17 - 2\vert=15$.

Step3: Calculate length of BC

Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ for points $B(2,15)$ and $C(17,7)$.
$BC=\sqrt{(17 - 2)^2+(7 - 15)^2}=\sqrt{15^2+( - 8)^2}=\sqrt{225 + 64}=\sqrt{289}=17$.

Step4: Calculate perimeter

Perimeter $P=AB + AC+BC=8 + 15+17 = 40$.

Answer:

40