Let the dimensions of the certificate be represented by x & y
given: perimeter is 30 inches. P = 2x + 2y
and area is 54 square inches A = xy
therefore 2x + 2y = 30 & xy = 54
solving for x, put y in respect to x, by dividing both sides of xy = 54 by x. y = 54/x
substitute the y value in 2x + 2y = 30
2x + 2(54/x) = 30
multiply the value of 2(54/x) = 108/x
2x + 108/x = 30
add the two terms on the left side with a common denominator of x and multiply both sides by x
2x² + 108 = 30x ==> x² - 15x + 54 = 0 (divide each term by 2 and subtract 15x from both sides)
(x - 9)(x - 6) = 0 (factor the left side of the equation)
x = 9 or x = 6 answer for one side of the certificate.
Now find the y value.
y = 54/x therefore when x = 9 then y = 6
or when x = 6 then y = 9.
the dimensions of the certificate is 9” by 6”
