Answer: 5cm and 8cm
Explanation:
Perimeter of a rectangle = 2l + 2w
Area of a rectangle = l × w
where l = length
w = width
Therefore,
2l + 2w = 26 ...... i
l × w = 40 ...... ii
We can reduce equation i to l + w = 13.
l + w = 13 ....... i
l × w = 40 ....... ii
From i, l = 13 - w ...... iii
Put the value of l into equation ii
l × w = 40
(13 - w) × w = 40
13w - w² = 40
13w - w² - 40 = 0
w² - 13w + 40 = 0
w² -8w -5w +40 = 0
w(w - 8) -5(w - 8) = 0
(w - 5) = 0 and (w - 8) = 0
w = 0 +5 and w = 0 + 8
w = 5
l = 8
The dimensions are 5cm and 8cm