The dimensions of the note card are length = 4 inches and width = 7 inches or length = 7 inches and width = 4 inches.
Let l be the length of the rectangular note card and w be its width.
Since the area of the rectangular note card is 28 square inches, we have that
lw = 28 (1)(the area of a rectangle).
Also, the perimeter of the rectangular note card is 22 inches. We have that
2(l + w) = 22 (2) (perimeter of a rectangle)
So, l + w = 11 (3)
From (3), l = 11 - w.
Substituting l into (1), we have
(11 - w)w = 28
11w - w² = 28
re-arranging, we have
w² - 11w + 28 = 0
Factorizing, we have
w² - 7w - 4w + 28 = 0
w(w - 7)- 4(w - 7) = 0
(w - 7)(w - 4) = 0
w - 7 = 0 or w - 4 = 0
w = 7 or w = 4
Since l = 11 - w,
substituting w = 7 into l, we have
l = 11 - 7 = 4 inches
substituting w = 4 into l, we have
l = 11 - 4 = 7 inches.
So, we have l = 4 and w = 7 or l = 7 and w = 4
So, the dimensions of the note card are length = 4 inches and width = 7 inches or length = 7 inches and width = 4 inches.
Learn more about rectangles here:
https://brainly.com/question/16031976
