Question

A community is building a square park with sides that measure 145 meters. To separate the picnic area from the play area, the park is split by a diagonal line from opposite corners. Determine the approximate length of the diagonal line that splits the square. If necessary, round your answer to the nearest meter.

145 meters
42,050 meters
205 meters
290 meters

Answer 1

The approximate length of the diagonal line that splits the square park is calculated using the Pythagorean theorem. Since both sides of the square are 145 meters, the length of the diagonal is found to be approximately 205 meters when rounded to the nearest meter.

Step-by-step explanation:

To find the approximate length of the diagonal line that splits the square park, we can use the Pythagorean theorem, which is applicable in a right-angled triangle. The square park has sides measuring 145 meters each, and the diagonal of the square will form two right-angled triangles. We can therefore calculate the diagonal as the hypotenuse of one of these triangles.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is expressed as c² = a² + b². Since the park is a square, both sides are equal, so a and b are both 145 meters.

Applying the Pythagorean theorem:

• a² = 145² = 21025
• b² = 145² = 21025

Now, add a² and b² to find c²:

c² = 21025 + 21025 = 42050

To find the length of the diagonal (c), we take the square root of c²:

c = √42050 ≈ 205 meters (rounded to the nearest meter)

Answer 2

You can solve this problem by using the pythagorean theorem.

`{a }^(2) + {b}^(2) = {c}^(2)`
Where the a- and b-values represent the sides of the triangle. Since the park is a sqaure, each side is equal. This means that both the a-value and the b-value are the same. Now, you must find the c-value.

145^2 + 145^2 = c^2

21,025 + 21,025 = c^2

42,050 = c^2 *now square root each side of the equation.*

205.06 = c

The length of the diagonal line is 205 meters.