The area of a rectangular living room is 50 square meters. The perimeter is 30 meters. What are the dimensions of the living room?

Question

i need help with this because i dont know what to do 

Answer 1

Here's what we know:

A = Lw (Area equals length times width)

A = 50 (Area equals 50 m²)

P = 2L + 2w (Perimeter equals the 2 lengths and widths added together)

P = 30 (perimeter equals 30 meters)

 

That gives us:

30 = 2L + 2w

Factor out 2:

15 = L + w

Isolate a variable:

L = 15 - w

 

Now to plug in the values into the area equations:

50 = w(15 - w)

Distribute:

50 = 15w - w²

Move everything to one side (add w², subtract 15w):

w² - 15w + 50 = 0

Factor out. We need numbers that when summed together make -15, and when multiplied equal 50:

(w - 10) (w - 5) = 0

You should certainly be able to see/solve what the dimensions are from here.