A rectangular certificate has an area of 54 square inches. Its perimeter is 30 inches. What are the dimensions of the certificate?

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”