SOLUTION: Two squares have total area 85 cm^2 and total perimeter 52 cm. what is the area in cm^2 of the large square ?

Question 316479: Two squares have total area 85 cm^2 and total perimeter 52 cm. what is the area in cm^2 of the large square ?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two squares have total area 85 cm^2 and total perimeter 52 cm.
what is the area in cm^2 of the large square ?
:
Let x = side of the large square
then
x^2 = it's area
:
Let y = side of small square
then
y^2 = it's area
:
"Two squares have total area 85 cm^2"
x^2 + y^2 = 85
:
" total perimeter 52 cm."
4x + 4y = 52
simplify, divide by 4
x + y = 13
y = (13-x)
:
replace y with (13-x) in the total area equation
x^2 + (13-x)^2 = 85
FOIL
x^2 + 169 - 26x + x^2 = 85
Combine as a quadratic equation
2x^2 - 26x + 169 - 85 = 0
2x^2 - 26x + 84 = 0
Factor this to
(2x-12)(x-7) = 0
Two solutions
x = 7
and
2x = 12
x = 6
:
Area of the larger square: 7^2 = 49 sq/cm
;
:
Check solution
y = 13-7
y = 6 cm
then 6^2 = 36cm is the small square area
total area: 49 + 36 = 85
:
Check the perimeter
49 + 36 = 85;
4(7) + 4(6) = 52

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