How to find dimensions?

Question

The perimeter of a rectangle is 26 and the area is 30. What are the dimensions of the rectangle? (please provide answer in following format: a x b).

Answer 1

P = 2a + 2b = 26, where a can be width or length; b is length or width.

Area = a•b = 30 Then a = 30/b

Substitute: 26 = 2(30/b) + 2b; 26 = 60/b + 2b

Mult both sides by b to elim the fraction: 26b = 60 + 2b²

Re-arrange in quadratic form: 2b² - 26b + 60 = 0

Divide by 2: b² - 13b + 30 = 0

Factor: (b - 3)(b - 10) = 0 So b = 3 or b = 10. If b = 3, then a = 10 and v.v. (Take your pick!)

Answer 2

Let x = the length and w = the width

Perimeter = 2x+2w=26

÷ through by 2

x+w=13 Eqn1

Area=xw= 30 Eqn2

w = 30/x

Substitute for w in Eqn 1

x + 30/x =13

x²-13x+30 = 0

(x-3)(x-10) = 0

x = 3,10

w =10,3

a×b = 3×10 or 10x3