2[L + W] =22
L*W = 28
W = 28/L sub this in the first equation
Solve for L:
2 (L + 28/L) = 22
Divide both sides by a constant to simplify the equation.
Divide both sides by 2:
L + 28/L = 11
Write the left hand side as a single fraction.
Bring L + 28/L together using the common denominator L:
(L^2 + 28)/L = 11
Multiply both sides by a polynomial to clear fractions.
Multiply both sides by L:
L^2 + 28 = 11 L
Move everything to the left hand side.
Subtract 11 L from both sides:
L^2 - 11 L + 28 = 0
Factor the left hand side.
The left hand side factors into a product with two terms:
(L - 7) (L - 4) = 0
Find the roots of each term in the product separately.
Split into two equations:
L - 7 = 0 or L - 4 = 0
Look at the first equation: Solve for L.
Add 7 to both sides:
L = 7 or L - 4 = 0
Look at the second equation: Solve for L.
Add 4 to both sides:
L = 7 or L = 4 and W=4 or W = 7