1) A square has a perimeter that is 1/8th its area. What is the side length of the square?
I'm not really sure how I would do this.
P = 2L+2W
A= LW or L^2
P= 1/8 Area
2) Lisa tells her dad that her age 5 years from now will be half his age then. If the dad's current age is D years, find Lisas age 5 years from now.
D= dad's current age
L= Lisa age
Not sure how to make the equations.
May I get help for these two questions please?
1. but it is square so L = W
p = 4 w
a = w^2
4 w = (1/8) w^2
32 w = w^2
w^2 - 32 w = 0
w(w-32) = 0
w = 0 or w = 32 use w = 32
p = 4w = 128
A = 32 *32 = 1024
1024/8 = 128 sure enough
L + 5 = (1/2)(D+5)
I want L+5 so it is (1/2)(D+5)
and that is all I can say with what I know.
Since it is a square, all four sides are equal
let each side be x
so perimeter = 4x
area = x^2
now it says: perimeter = 1/8 of the area
4x = (1/8)x^2
multiply each side by 8
32x = x^2 , divide by x
32 = x , and there you have it !
Dad's current age ---- D
Dad's age 5 years from now ---- D+5
Lisa's age 5 years from now = (1/2)(D+5) = (D+5)/2
We can't have an actual age since some information is missing.
e.g. if her Dad is now 35 , he will be 40 in five years, and Lisa's age in 5 years is 20. He is now 35 and she now is 15.
if her Dad is now 41 , he will be 46 in five years, and Lisa's age in 5 years is 23. He is now 41 and she is now 18.
Notice that there are many possible answers, but they have to be reasonable.
e.g. if Dad is now 19, he will be 24 in 5 years, which would make Lisa 12 in five years and her present age as 7. That would mean that Dad was 12 when Lisa was born. Possible, but not likely.
posted by Reiny