Question

Quadrilateral ABCD is the figure below represents a scaled-down model of a walkway around a historic site. quadrilateral EFGH represents the actual walkway. ABCD is similar to EFGH.

What is the total length, in feet, of the actual walkway. Numerical answers only.

Answer 1

Answer:

192 feet

Step-by-step explanation:

Since we know that ABCD and EFGH are similar, they are just scaled differently, we know the ratio between each corresponding segment will be the same.

If we take corresponding segments AB and EF, we know that AB is 6 inches, and that EF is 72 feet, so the ratio is 144 (72/6 = 12, then 12 inches per foot).  To make it simple, let's say 12... and we change the unit from ft to inches. Meaning EF is 12 times longer (in feet) than AB is (in inches).

So, the lengths of the actual pathway are:

EF = 72 ft

FG = 36 ft (3 * 12)

GH = 36 ft (3 * 12)

EH = 48 ft (4 * 12)

So, the total length of the pathway is: 72 + 36 + 36 + 48 = 192 feet

Answer 2

Answer:

192 ft

Step-by-step explanation:

If the figure A and the figure B are similar in scale k, then the ratio corresponding sides is equal k, and the ratio of perimeter is equal to k.

Calculate the scale:

$k=\dfrac{72\ ft}{6\ in}=\dfrac{(72)(12)\ in}{6\ in}=\dfrac{864}{6}=144$

Lets P₂ - the perimeter of the quadrilateral EFGH.

Calculate the perimeter of the quadrilateral ABCD:

P₁ = 3 + 3 + 6 + 4 = 16 in.

Substitute to:

$\dfrac{P_2}{P_1}=k$

$\dfrac{P_2}{16}=144$      multiply both sides ny 16

$P_2=2304\ in$

Convert to the feet:

$P_2=2304:12=192\ ft$