Question

PLEASE HELP IM BEING TIMED! Geometry!! Answer needs to be in feet.

On the map below, 51st St. and 52nd St. are parallel.
Ms. Lovely walks from point A to point B and then walks to point C.
Mr. Peterson walks directly from point A to point C.
How much farther did Ms. Lovely walk than Mr. Peterson?
Park Ave
600
51 St
300
500
52 St
12001
4
Wayne St

Answer 1

Ms.Lovely walked an extra distance of 600 ft

Explanation:

Here, we want to calculate how much Farther did Ms lovely walked

she walked from A to B and then to C

The total distance she covered will be;

1,200 + 300 + 600 = 2,100 ft

We are told that Mr Peterson walked directly from A to C

what we can see above is too similar triangles

The bigger CAB and the smaller one above it

Let us have the total length of AC as (x + 500)

Since the two triangles are similar, the ratio of their sides are equal

Thus;

900/x + 500 = 600/x

900x = 600(x + 500)

900x = 600x + 300,000

900x-600x = 300,000

300x = 300,000

x = 300,000/300

x = 1000

So the total distance she walked from A to C will be ;

x + 500 = 1000 + 500 = 1,500 ft

So the distance she walked more will be (Ms.Lovely)

= 2,100 ft - 1,500 ft = 600 ft