A chalkboard has a perimeter of 20 feet and an area of 24 square feet. What are the dimensions of the board?

Question

I dont know how to do this please just give me that answer to the problem

Answer 1

Let w = the width of the chalkboard

Let L = the length of the chalkboard

P = 2L + 2w         A = Lw

20 = 2L + 2w       24 = Lw     or    L = 24/w

20 = 2(24/w) + 2w

       Multiply both sides by w

20w = 48 + 2w²

2w² - 20w + 48 = 0    

       Divide both sides by 2.

w² - 10w + 24 = 0

(w - 6)(w - 4) = 0

w - 6 = 0     and   w - 4 = 0

 w = 6 feet              w = 4 feet

L = 24/w = 24/6 = 4 feet       L = 24/w = 24/4 = 6 feet

Thus, the dimensions are 4 feet by 6 feet.