Answer:
23. Length = 21 feet, Width = 3 feet
24. Larger Angle = 162 degrees, Smaller Angle = 18 degrees
Step-by-step explanation:
23.
Let us say: l ⇒ length of the rectangular pool, w ⇒ width of the rectangular pool
According to the problem we could formulate two equations as such:
2l + 2w = 48,
l = 15 + 2w
Now let us solve for the dimensions;
First convert the two equations to standard form:
2l + 2w = 48,
l - 2w = 15
Using process of elimination:
2l + 2w = 48
+ l - 2w = 15
Simplify:
3l = 63,
length = 21 feet
Substitute this value of length into the second equation.....:
21 - 2w = 15
.......And simplify:
-2w = -6,
width = 3 feet
24.
Let us say: L ⇒ larger angle, S ⇒ smaller angle,
According to the problem we could formulate two equations as such:
L + S = 180,
L = 9S
Now let us solve for the angles;
Let us here use substitution:
(9S) + S = 180
Simplify:
10S = 180,
Smaller Angle = 18 degrees
Substitute this value of the smaller angle into the second equation.....:
L = 9(18)
.......And simplify:
Larger Angle = 162 degrees
