Answer:
7. 29 cm
8. equation: 61 = (x) +(2x -7) +(3x +2); sides 11, 15, 35
Explanation:
7. Let w represent the width. The length is 3 less than twice the width, so the length is 2w-3. The perimeter is given by the formula ...
P = 2(L+W)
Substituting the known values, we have ...
90 = 2((2w-3) +w)
45 = 3w -3 . . . . . . . . divide by 2
15 = w - 1 . . . . . . . . . .divide by 3
16 = w . . . . . . . . . . . . add 1
L = 2w -3 = 2(16) -3 = 29
The length of the rectangle is 29 cm.
__
8. The equation that should be used is the one that relates the side lengths to the perimeter.
P = a + b + c . . . . for sides a, b, c
61 = (x) +(2x -7) +(3x +2)
61 = 6x -5 . . . . . . collect terms
66 = 6x . . . . . . . . add 5
11 = x . . . . . . . . . . divide by 6
Then the side lengths are ...
a = x = 11
b = 2x -7 = 2(11) -7 = 15
c = 3x +2 = 3(11) +2 = 35
_____
Comment on problem 8
You will notice that the side lengths do not satisfy the triangle inequality: the sum of the short sides is not greater than the long side. These side lengths cannot form a triangle. Cute algebra, but bad geometry.