Math Help Please?

Question

Writing: Find the length of a side of a square whose perimeter and area are the same number, though not the same unit.Explain your reaoning.

Answer 1

4x = x^2

x = 4

Perimeter is 4 units, area is 4 units^2

Trick question.

Answer 2

Be a the side

The perimeter is 4a
The area is a^2

Let a be the side length in cm = 4*10^n

The perimeter is 16*10^n

Let s be the area in m^2, s=(a/100)^2 = [4*10^(n-2)]^2 =
= 16 * 10^(2n - 4)

16*10^n = 16*10^(2n - 4) // divide by 16

10^n = 10^(2n - 4) // take logs

n = 2n - 4 // -n

0 = n-4

n=4

a=4*10^4 = 40,000 cm

The perimeter is 160,000 cm

The area is 16*10^8 cm^2 = 16*10^4 m^2 = 160,000 m^2

Answer 3

If L = length of one side.

4L = perimeter of square
L^2 = area of square

So 4L = L^2 => L(L-4) = 0

So either the square has sides of length 0 - not real square
Or L=4

Check: perimeter=4x4=16
Area = 4^2 = 16

Answer 4

A square of sides 4 inches has a perimeter of 16 inches and an area of 16 inches^2.

Perimeter a is 4 * side inches
Area is side^2 inches^2

so you need 4 * side = side^2
divide each by side and get side = 4 inches

Answer 5

YOU WANNA KNOW WHEN WILL THE PERIMETER EQUAL THE AREA SO SET THE FORMULAS EQUAL TO EACH OTHER...

W + W + L + L = WL

SINCE A SQAURE IS ALL THE SAME SIZE THE W = L

W + W + W + W = WXW

4W = WXW

4W = W^2

GET INTO QUADRATIC FOR,....

W^2 - 4W = 0

FACTOR

W(W-4) = 0
W = 0
W- 4 = 0
+ 4 +4
-------------
W = 4

SP A SIDE LENGTH - 0 DOESNT MAKE SINCE...

SO THE ONLY POSSIBILTY IS W = 4

SO WHEN A SIDE OF A SQAURE IS 4 UNITS THE AREA AND PERIMETER ARE BOTH 16.

ANSWER = 4

Answer 6

find l that a square with l length sides has a=p

a=l^2
p=l(4)

l^2=l(4)
l=4
l=4 units

but for area it would be 4 units^2
and perimeter would be just 4 units.

Edit: oops. first said area was unit^3 which is dumb.