Answer:
Part A: the length of each side of the square ABCD = 14 units
Part B: the length of the diagonal of the square ABCD = 14√2 ≈ 19.8 units
Explanation:
Part A: Find the length of each side of the square ABCD
Let the point between A and B ⇒ O , see the attached figure.
As shown:
AOW is a right triangle at angle O
So, (AO)² = (AW)² - (OW)² = 13² - 12² = 25
∴ AO = √25 = 5
And, BOW is a right triangle at angle O
So, (BO)² = (BW)² - (OW)² = 15² - 12² = 81
∴ AO = √81 = 9
∴ AB = AO + OB = 5 + 9 = 14
So, the length of each side of the square ABCD = 14 units
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Part B: Find the length of the diagonal of the square ABCD
The diagonal is AC
Since the four angles of the square are right angles
So, ABC is a right triangle at angle B
And AB = BC = 14
So, (AC)² = (AB)² + (BC)² = 14² + 14² = 2 * 14²
∴ AO = √(2 * 14²) = 14√2 ≈ 19.8
So, the length of the diagonal of the square ABCD = 14√2 ≈ 19.8 units