Question 229539
An area of 52 square feet is to be enclosed by two squares whose sides are in the ratio of 2:3.
Find the sides of the two squares.
:
Let x = side of one square
Let y = side of the other squares
then
{{{x/y}}} = {{{2/3}}}
therefore
2y = 3x
y = {{{3/2}}}x
y = 1.5x
:
Area of the two squares:
x^2 + y^2 = 52
Replace y with 1.5x
x^2 + (1.5x)^2 = 52
x^2 + 2.25x^2 = 52
3.25x^2 = 52
x^2 = {{{52/3.25}}}
x^2 = 16
x = {{{sqrt(16)}}}
x = 4 ft side of one square
and
y = 1.5(4)
y = 6 ft side of the other square
;
:
Check solution: 4^2 + 6^2 = 52