Algebra II?

Question

How would you set up an equation for this word problem?

The perimeter of a square is 12 meters greater than the perimeter of another square. Its area is 45 square meters greater than the area of the smaller square. Find the perimeter of each square.

Answer 1

side of 1st square = a
side of 2nd square = b

P of 1st = 4a
P of 2nd = 4b

1. 4a = 4b + 12 ; first equation

A of 1st = a^2
A of 2nd = b^2

2. a^2 = b^2 + 45 ; second equation

4a - 4b = 12
a^2 - b^2 = 45 ; align as a system of equations with two unknowns

a - b = 3 -> a=b + 3 ; substitute for "a", solve for "b"
(b+3)^2 - b^2 = 45
b^2 + 6b + 9 - b^2 = 45
6b = 36
b = 6

a - b = 3 ; substitute "b", solve for "a"
a - 6 = 3
a = 9

P of 1st = 4a = 4*9 = 36
P of 2nd = 4b = 4*6 = 24 ; find the perimeters

Answer 2

let x be one the smaller square
let y be the larger square

x/4 is the side of the smaller square
y/4 is the side of the larger square

The perimeter of a square is 12 meters greater than the perimeter of another square.
y = x + 12

Its area is 45 square meters greater than the area of the smaller square
(y/4)^2 = (x/4)^2 + 45
y^2/16 = x^2/16 + 45
y^2 = x^2 + 720

(x + 12)^2 = x^2 + 720
x^2 + 24x + 144 = x^2 + 720
24x + 144 = 720
24x = 576
x = 24

smaller square: 24m
larger square: 36m

Answer 3

Let x = side of greater square, y = side of smaller square.

2(2y) + 12 = 2(2x)
4y + 12 = 4x
y + 3 = x
y = x - 3

(x - 3)^2 + 45 = x^2
x^2 - 6x + 9 + 45 = x^2
- 6x = - 54
x = 9

Answer:
Perimeter of larger square:
= 9 * 4
= 36 meters

Perimeter of smaller square:
= (9 - 3) * 4
= 6 * 4
= 24 meters

Answer 4

x = perimeter of smaller square
x+ 12 = perimeter of larger square
(x/4)^2 = area of smaller square
[(x+12)/4]^2 = area of larger square
[(x+12)/4]^2 - (x/4)^2 = 45
(x^2+24x+144)/16 - x^2/16 = 45
24x+144 = 16*45 = 720
24x = 720-144=576
x = 24 = perimeter of smaller square
x+12 = 36 = perimeter of larger square

Answer 5

I was really good at math in high school/college but It's been a while but this is what I came up with;

4x + 12 = 4y
y(squared) + 45 = x(squared)

Sorry I dont know how to do the little 2 on my computer!

Try that, sorry if it's wrong...

Answer 6

4a -- 4b = 12m => (a -- b) = 3m
a^2 -- b^2 = 45 m^2
=> (a + b)(a -- b) = 45 m^2
=> (a + b)(3m) = 45 m^2
=> (a + b) = 15m
adding (a + b) = 15m and (a -- b) = 3m
2a = 18m => a = 9m and b = (15 -- 9)m=6m
Perimeters are 4a = 4(9m) = 36m
and 4b = 4(6m) = 24m
36 m and 24 m answers