10 troy is building a rectangular garden that is
10 feet by 6 feet. what should be the length
of the diagonals to ensure a 90 degree angle?

  to ensure 90° corners, the lengths of the diagonal should be the same

Step-by-step explanation:

The Pythagorean theorem can be used to find the expected length of the diagonal. It tells you the square of the diagonal is the sum of the squares of the sides:

  d² = (10 ft)² + (6 ft)² = 136 ft²

  d = √136 ft ≈ 11.6619 ft ≈ 11 ft 7 15/16 in

The length of each diagonal should be very nearly 11 feet 7 15/16 inches.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2  

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation: