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
P=1/8 (L^2)
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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
so
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
check
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.
Sure! Let's break down each problem and explain the steps to find the answers.
1) To find the side length of the square, we need to set up an equation using the given information about the perimeter and area.
Let's start by assigning a variable to the side length of the square. Let's call it "s".
The perimeter of a square is calculated by multiplying the side length by 4. So, the perimeter of our square is 4s.
The area of a square is calculated by multiplying the side length by itself. So, the area of our square is s^2.
Now, the problem states that the perimeter of the square is 1/8th of its area. So, we can set up the equation:
4s = (1/8) * s^2
To solve this equation, we can multiply both sides by 8 to get rid of the fraction:
32s = s^2
Next, we can rearrange this equation to bring all the terms to one side:
s^2 - 32s = 0
Now, we can factor out an "s" from the left side:
s(s - 32) = 0
Since the product of two numbers is zero only if at least one of the numbers is zero, we can set each factor equal to zero:
s = 0 or s - 32 = 0
Since the side length cannot be zero (as that would be a degenerate square), we discard the solution s = 0. Therefore, the side length of the square is:
s = 32 units
So, the side length of the square is 32 units.
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2) To find Lisa's age 5 years from now, we need to set up an equation using the given information about Lisa's and her dad's ages.
Let's assign a variable to Lisa's current age. Let's call it "L".
The problem states that Lisa's age 5 years from now will be half her dad's age then. So, we can set up the equation:
L + 5 = (1/2) * (D + 5)
Here, "D" represents the dad's current age.
To solve this equation, we can simplify it:
2(L + 5) = D + 5
Expanding the left side:
2L + 10 = D + 5
Now, let's isolate Lisa's age. Subtracting 10 from both sides:
2L = D - 5
Dividing both sides by 2:
L = (D - 5)/2
So, Lisa's age 5 years from now is given by the expression (D - 5)/2.
I hope this helps! Let me know if you have any further questions.