The questions are about pythagorean triple

Question

Answer 1

10: It is isosceles triangle (both angles 45 degrees).

V = 6√2

U = √144 = 12 ← from Pythagorean theorem

12: Isosceles triangle.

x = y

√2x² = 18√2, x√2 = 18√2, x = 18

13: Isosceles triangle.

x = y

√2x² = 15, x = 15/√2

14: Isosceles triangle.

x = y

x =20/√2

Answer 2

11) 45-45-90 right triangle. Lengths of legs are equal so v = 6 sqrt(2)

length of hypotenuse is sqrt(2) * length of legs so u = 6 sqrt(2) sqrt(2) = 12

12) 45-45-90 right triangle. Lengths of legs are equal and equal to hypotenuse / sqrt(2) = 18 sqrt(2)/sqrt(2) = 18 so x and y = 18.

13) 45-45-90 right triangle. Lengths of legs are equal and equal to hypotenuse / sqrt(2) = 15/sqrt(2) = 15sqrt(2)/2, so x and y = 15sqrt(2)/2.

14) 45-45-90 right triangle. Lengths of legs are equal and equal to hypotenuse / sqrt(2) = 20/sqrt(2) = 20sqrt(2)/2 = 10sqrt(2), so x and y = 10sqrt(2).

Answer 3

These are not Pythagorean triples; Pythagorean triples are integers which together form a right angle: examples are (3, 4, 5), (6, 8, 10), (5, 12, 13), (7, 24, 25)

Your 4 problems are all iscosceles right triangles - right triangles whose angles are 45°, 45°, 90°

Their sides are in the ratio 1:1:√2

Thus,

11. v has the same length as the given side, 6√2 u = 6 √ 2 * √2 = 6 * 2 = 12

12.y and x each have the length 18√2 / √2 = 18

13.x and y have length 15/√2 or 15√2/2

14.u and v have length 20/√2 = 10√2