Jayden H. answered • 09/11/15

I am patient and love helping people learn.

Brennan,

Step 1: Define perimeter and area in the context of a rectangle in equation form.

Perimeter of a rectangle: side 1 + side 2 + side 3 + side 4 = Perimeter. (likely you know this already) Side 1 = side 3 and side 2 = side 4 so the equation can be simplified to: short side (S)*2 + long side (L)*2 = Perimeter (P).

Area of a rectangle: base (S) * height (L) = Area (A).

In summary: P = S*2+L*2 and A = S*L

Step 2: Fill in the equations with numbers from the question and see if we can find the other variables using algebra.

P = 34 ft = S*2 + L*2

A = 30 ft^2 = S*L

We have two variables we must solve for but thankfully we also have two equations.

Step 3: Solve for the unknowns.

34 = 2S + 2L

30 = S*L

(Note: I have dropped the units for simplicity in working out the equations, don't forget them though)

I will use substitution.

L = 30/S

34 = 2S + 2*(30/S) = 2S + 60/S Multiply the S through and rearrange.

0 = 2S^2 - 34S + 60

0 = S^2 - 17S + 30 Two possible answers are found.

S = (2, 15) (Note: not an ordered pair)

30 = (2, 15)*L

L = (15, 2)

L = 15 ft

S = 2 ft (just because 15 > 2).

Brennan K.

09/11/15