Rectangular triangle, with an acute angle of 45 degrees, the hypotenuse of 8 cm, the midlines are drawn.

Rectangular triangle, with an acute angle of 45 degrees, the hypotenuse of 8 cm, the midlines are drawn. Find the perimeter of the triangle formed with the midlines.

From the condition it is known that the triangle is rectangular, it is also known that the acute angle is 45 °, the hypotenuse is 8 cm.
Find all the corners of the triangle.
Δ ABC – rectangular, that is, angle ∠ A = 90 °; ∠B = 45 °, therefore
∠ C = 90 ° – ∠ B = 90 ° – 45 ° = 45 °.
We conclude that Δ ABC is rectangular and isosceles, that is, AC = AB.
Let’s apply the Pythagorean theorem to calculate AB:
AB = AC = 8: √2 = 4√2 cm.
Let’s find the middle lines KN and NM are equal to half of the legs AC = BC ⇒ KN = NM = 4√2 / 2 = 2√2 cm.
We also find the middle line KM, which is equal to half of the hypotenuse BC:
KM = 8/2 = 4 cm.
It remains to find the perimeter Δ KNM:
P = 4 + 2 * 2√2 = 4 + 4√2 = 4 (1 + √2) see.