Area of square = s^2 Area of Rectangle = lw l = 2s
w+3 = s solve for w, w=s-3 Now we have l and w. Plug both into area of rectangle formula so: (2s)(s-3) Since both areas are equal set both equations equal to each other: (2s)(s-3)=s^2 Now simplify 2s^2-6s=s^2 s^2-6s=0, Solve for s. Factor polynomial. s(s-6)=0 , s can be equal to 0 or 6. HOWEVER, you cannot have a side length of 0 therefore the side length has to be 6. Now plug in s for the length formula for the rectangle: l = 2s so... l = 2(6) so length of rectangle = 12. Now plug in s for the width formula for the rectangle: w+3=s so... w+3=6 so width of rectangle = 3. Now the dimensions of the rectangle are 12 by 3. 12 being length and 3 width. To CHECK: Find area of rectangle: A=lw so A=3 times 12 so A=36 Find area of square: We know the side is equal to 6 so A=s^2 so 6^2 = 36 The areas are equal that verifies the answer of 12 by 3.
