A rectangular field is nine times as long as it is wide. If the perimeter of the field is 1700 feet, what
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Refer to the figure given below while reading the solution.
Suppose the dog reaches position A when traveled 10 m diagonally towards the opposite side.
And then position B when traveled 5 m towards the right turning 90°.
We can observe that APC is a right triangle with legs of equal length AC. And the coordinates of the point A is (AC, AC).
Also we can observe that APB is a right triangle with legs of equal length AD. Then the coordinates of the point D is (AC, AC-AD).
Hence, the coordinates of B will be (AC+AD, AC-AD).
Now, we since we have the coordinates we can calculate the shortest distances of B from each of the sides.
- The shortest distance of B from PQ = AC-AD
- The shortest distance of B from SR = 44-(AC-AD)
- The shortest distance of B from SP = AC+AD
- The shortest distance of B from RQ = 44-(AC+AD)
So, the average of the shortest distances of B from each side is
Hence, the average of the shortest distance of B from each side is 22 m
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corresponding angles, therefore
m∠1 = m∠2 → m∠2 = 130°
vertical angles, therefore
m∠2 = m∠3 → m∠3 = 130°
If ∠1 and ∠2 are complementary, then m∠1 + m∠2 = 90°.
If ∠2 and ∠3 are complementary, then m∠2 + m∠3 = 90°
Therfore