Answer:
6.83 units
Step-by-step explanation:
Let the height of the original pyramid be represented by h. Then the cut off top has a height of (h -2). The scale factor for the area is the square of the scale factor for height, so we have ...
(height ratio)^2 = 1/2
((h -2)/h)^2 = 1/2
(h -2)√2 = h . . . . . . square root; multiply by h√2
h(√2 -1) = 2√2 . . . . add 2√2 -h
h = (2√2)/(√2 -1) ≈ 6.8284 . . . units
The altitude of the original pyramid is about 6.83 units.
Area of square = s^2
Area of Rectangle = lw
l = 2s
w+3 = s
solve for w, w=s-3
Now we have l and w.
Plug both into area of rectangle formula so: (2s)(s-3)
Since both areas are equal set both equations equal to each other:
(2s)(s-3)=s^2
Now simplify
2s^2-6s=s^2
s^2-6s=0, Solve for s.
Factor polynomial. s(s-6)=0 , s can be equal to 0 or 6. HOWEVER, you cannot have a side length of 0 therefore the side length has to be 6.
Now plug in s for the length formula for the rectangle:
l = 2s so... l = 2(6) so length of rectangle = 12.
Now plug in s for the width formula for the rectangle:
w+3=s so... w+3=6 so width of rectangle = 3.
Now the dimensions of the rectangle are 12 by 3. 12 being length and 3 width.
To CHECK:
Find area of rectangle:
A=lw so A=3 times 12 so A=36
Find area of square:
We know the side is equal to 6 so
A=s^2 so 6^2 = 36
The areas are equal that verifies the answer of 12 by 3.
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Answer:
y=-1(1)/(5)
Step-by-step explanation:
