Question

This is due tomorrow

A path goes around a triangular park, as shown.


a. Find the distance around the park to the nearest yard.
( I counted and got 190 that's not correct)
b. A new path and a bridge are constructed from point Q to the midpoint M of PR.
Find QM to the nearest yard.
(I counted and got 30 also not correct)

Answer 1

Explanation:

the two sides are 50 and 80

Use Pythagorean theorem

It’s about 94.34 (94)

So I’d guess 224

Answer 2

a. The distance around the park to the nearest yard is equal to 191 yards.

b. Since a new path and a bridge are constructed from point Q to the midpoint M of PR, the length of QM is 40 yards.

Part a.

In Mathematics and Geometry, Pythagorean theorem is an Euclidean postulate that can be modeled or represented by the following mathematical equation:

`c^2=a^2+b^2`

Where:

• a is the opposite side of a right-angled triangle.
• b is the adjacent side of a right-angled triangle.
• c is the hypotenuse of a right-angled triangle.

In order to determine the distance around the park, we would have to apply Pythagorean's theorem as follows;

`PR^2=PQ^2+QR^2\\\\PR^2=40^2+70^2\\\\PR^2=1600+4900\\\\PR=√(6500)`

PR = 80.6226 ≈ 81 yards.

Total distance (perimeter of triangle PQR) = PQ + QR + PR

Total distance (perimeter of triangle PQR) = 40 + 70 + 81

Total distance (perimeter of triangle PQR) = 191 yards.

Part b.

Since triangle PQR is a right-angled triangle and based on the definition of a midpoint, we have;

QM = 1/2 × PR

QM = 1/2 × 80.6226

QM = 40.3113 ≈ 40 yards.