Answer:
a) Yes
b) No
c) Yes
d) No
e) No
Step-by-step explanation:
Right triangle:
The square of the larger side is equals to the sum of the squares of the smaller sides.
a. 6, 8, 10
The answer is yes.
b. 8, 15, 16
So no.
c. 10, 24, 26
So yes
d. 20, 21, 28
So no.
e. 9, 35, 41
================================================================
Explanation:
Refer to the diagram below. The width is w. We have two opposite and parallel sides equal to this. The other two parallel congruent sides are L = 25-2w meters long. We start with the total amount of fencing, and then subtract off the two width values, so 25-w-w = 25-2w.
The area of the rectangle is
Area = length*width
Area = L*W
Area = (25-2w)*w
Area = 25w - 2w^2
Area = -2w^2 + 25w
Set this equal to the desired area (25 square meters) to get
-2w^2 + 25w = 25
and we can subtract 25 from both sides to get everything on one side
-2w^2 + 25w - 25 = 0
side note: The two approximate solutions of this equation are w = 1.0961 and w = 11.4039 (use the quadratic formula or a graphing calculator to find this)
