Answer:
4 cm by 9 cm
Step-by-step explanation:
The formula for area of a rectangle is A = LW, where L and W are the dimensions of the rectangle. We have
36 = LW
The formula for perimeter of a rectangle is P = 2L + 2W. We have
26 = 2L + 2W
Solve the area formula for any variable..
36/L = W
Plug that into the perimeter equation..
26 = 2L + 2(36/L)
Now simplify...
26 = 2L + 72/L
Multiply all 3 terms by L to get rid of the fraction...
26L = 2L² + 72
Now this is a quadratic equation, get all terms to one side and solve...
2L² - 26L + 72 = 0
Divide both sides by 2
L² - 13L + 36 = 0
Factor the left side
(L - 9)(L - 4) = 0
So L = 4, or 9
If L = 4, then W = 36/4 = 9
If L = 9. then W = 36/9 = 4
either way, the dimensions are 4 cm by 9 cm
