Question

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A 5 mile jogging path diagonally divides a rectangular park in half. The park is 4 miles long.
Find the width of the park.​

Answer 1

Answer:

3 miles

Step-by-step explanation:

Given that a 5 mile jogging path diagonal divides a rectangular park in half and the park is 4 miles long.

We are to find the width of the park.

As shown in the attached figure below, the diagonal BD divides the rectangle ABCD into two equal parts,

where length DA = a = 4 miles, BD = b = 5 miles and AB = c = width = ?

Since each angle of a rectangle is right-angle, so triangle ABD will be a right-angled triangle.

Using Pythagoras theorem in triangle ABD, we have

${b}^{2} = {c}^{2} + {a}^{2}$

${5}^{2} = {c}^{2} + {4}^{2}$

$25 = {c}^{2} + 16$

${c}^{2} = 25 - 16$

${c}^{2} = 9$

$c = \sqrt{9}$

$c = 3$

therefore the width is 3 miles.

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