A rectangle has an area of 30 square feet meters and a perimeter of 34meters. What are the dimensions of the rectangle?

Question

What is the dimensions of a rectangle the has an area of 30 square feet and a perimeter of 34 meters.

Answer 1

so a rectangle has two sets of side lengths that are unknown. One set has 2 longer sides and the other has 2 shorter sides. So there are two unknowns - the lengths of each of the different sides. Let x  be the length of one of the sides. Let y be the length of one of the other sides.  

 

Then you have two equations:

 

Perimeter = 2*x + 2*y  = 34

Area = x*y = 30

I get that one of the smaller sides is 2 and one of the bigger sides is 15. They fit the equations.

 

Hint: Solve the two equations.  Replacing one in the other you get:

 

   0 = x^2+30-17x