Question

Given: Elmwood St. and Oak Dr. are the same distance. All intersections are perpendicular.

Prove: Peach Tree Dr. is the same distance as Sycamore Ln.

Answer 1

Answer:

The above result is proved with the help of Pythagoras theorem and explained below.

Step-by-step explanation:

Given figure ABCD in which AD=BC and all angles intersect at right angle. Hence, the triangle formed inside ADC and ABC are right angled triangle.

In triangle ADC,

By applying Pythagoras theorem, we get

$AC^{2}=AD^{2}+DC^{2}$    →  (1)

In triangle ABC,

$AC^{2}=AB^{2}+BC^{2}$    →  (2)

Now, from eq (1) and (2)

Peach Tree Dr. is the same distance as Sycamore Ln.

$AD^{2}+DC^{2} = AB^{2}+BC^{2}$

⇒ $DC^{2} = AB^{2}$              (∵ AD=BC)

⇒ DC=AB                    (∵Distance can never negative)

Therefore, Peach Tree Dr. is the same distance as Sycamore Ln.