In the diagram below, TUVW is a rectangle. Prove triangle TZW is congruent to triangle UZV.
1 answer:
Answer:
By S.S.S. congruence property; ΔTZW ≅ ΔVZU
Step-by-step explanation:
Given:
TUVW is a rectangle.
To Prove : TZW ≅ UZV
Proof:
Since TUVW is a rectangle, and we know that opposite side of a rectangle is equal.
So,
And also TV and WU are the diagonals of the rectangle.
And the diagonals of rectangle bisects each other.
Therefore;
Now In ΔTZW and ΔVZU
TW = UV (from 1)
TZ = ZV (from 2)
WZ = ZU (from 3)
So, by S.S.S. congruence property;
ΔTZW ≅ ΔVZU
Hence proved.
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Answer:
outer width of trough = outer height of trough = x = 4ft
outer length of trough = 2x = 8ft
Step-by-step explanation:
Let,
x = outer width of trough = outer height of trough
Now, according to given condition:
2x = outer length of trough
Now we calculate the inner dimensions by subtracting the thickness (1 ft)
Therefore,
x - 2(1ft) = x - 2ft = inner width of trough (because 1ft from both sides will be subtracted)
x - 1ft = inner height of trough (because only bottom thickness will be subtracted)
2x - 2ft = inner length of trough (because 1ft from both sides will be subtracted)
Now, for the holding volume or inside volume of trough will be:
So, we will have three roots from this solution. Two, of them will be complex from the second factor. So, we ignore them and take the third one as our answer:
x - 4 = 0
x = 4ft
Now the outer dimensions will be:
<u>outer width of trough = outer height of trough = x = 4ft</u>
<u>outer length of trough = 2x = 8ft</u>