Answer:
3.6 m
Step-by-step explanation:
Given that :
Length of room = 6
Distance between opposite corners = 7
Width of room :
Using Pythagoras rule:
Opposite ²= hypotenus² + adjacent²
From. The diagram attached :
w² = 7² - 6²
w² = 49 - 36
w² = 13
w = 3.605
w = 3.6 m
The perimeter of right isosceles ΔABC with midsegment DE is 16 + 8√2.
If right isosceles ΔABC has hypotenuse length h, then the two other sides are congruent.
side a = side b
Using Pythagorean theorem, c^2 = a^2 + b^2
h^2 = a^2 + b^2 a = b
h^2 = 2a^2
a = h/√2
If DE is a midsegment not parallel to the hypotenuse, then it is a segment that connects the midpoints of one side of a triangle and the hypotenuse. See photo for reference.
ΔABC and ΔADE are similar triangles.
a : b : h = a/2 : 4 : h/2
If a/2 = a/2, then b/2 = 4.
b/2 = 4
b = 8
If a = b, then a = 8.
If a = h/√2, then
8 = h/√2
h = 8√2
Solving for the perimeter,
P = a + b + h
P = 8 + 8 + 8√2
P = 16 + 8√2
P = 27.3137085
To learn more about midsegment: brainly.com/question/7423948
#SPJ4
