Please help a 15 pointsRectangle R has varying length l and width w but a constant perimeter of 4 ft.a. Express the area A as a function of l. What do you know about this function?b. For what values off and w will the area of Rbe greatest? Give an algebraicargument. Give a geometric argument.

Answer:a. A = l(2 - l)b. l = 1 foot and w = 1 foot.Step-by-step explanation:With a constant perimeter of 4 feet, a rectangle has variable length l and variable width w. So, 2(l + w) = 4 ⇒ l + w = 2 .........(1) ⇒ w = 2 - l ........(2) a. Now, area of the rectangle will be A = lw = l(2 - l) ......... (3) {From equation (2)} b. For A to be maximum, the condition is [tex]\frac{dA}{dl} =0[/tex]. Now, from equation (3), differentiating with respect to l, we get [tex]\frac{dA}{dl} =2-2l = 0[/tex]. ⇒ l = 1 feet. Hence, w = 1 feet. So, when the length and width of the rectangle are the same and equal to 1 foot, then only the area will be maximum. That means, when the rectangle becomes a square, then the area will be maximum.