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A rectangular note card has an area of 18 square inches. Its perimeter is 18 inches. What are the dimensions of the note card? inches by inches

Respuesta :

let the length be x and width be y

Perimeter is 18 inches
2x + 2y = 18

Area is 18 square inches
xy= 18

2x + 2y = 18 ---------- (1)
xy= 18 ------------------ (2)

From (2):
xy = 18
x = 18/y ------- sub into (1)
2(18/y) + 2y = 18

multiply by y through
36 + 2y^2 = 18y
2y^2 - 18y + 36 = 0

Divide by 2 through
y^2 - 9y + 18 = 0
(y - 3)(y - 6) = 0
y = 3 or y =6

If y = 3 --- sub into (2)
3x = 18
x = 6

If y = 6 .----- sub into (2)
6x = 18
x = 3

So the two dimension is 3 and 6 inches.

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