Among all rectangles that have a perimeter of 176 , find the dimensions of the one whose area is largest. Write your answers as fractions reduced to lowest terms.

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Vaing1990 · Accepted Answer

Step 1 Given: Perimeter of the rectangle is, P=176 units Step 2 Perimeter of the rectangle is, P=176 units Let the length =x units Let the width =y units Perimeter of the rectangle is given by: ⇒2(x+y)=P ⇒2(x+y)=176 ⇒x+y=1762 ⇒x+y=88 ⇒y=88−x..............(i) Area of the rectangle is given by: ⇒A=xy Put y=88−x from (i): ⇒A=x(88−x) ⇒A=88x−x2 Step 3 To maximize the area: ⇒dAdx=0 d(88x−x2)dx ⇒88−2x=0 ⇒−2x=−88 ⇒x=−88−2 ⇒x=44 Put x=44 in (i): ⇒y=88−44 ⇒y=44 So, the dimensions of the rectangle with the largest area are: ⇒44 units×44 units

Among all rectangles that have a perimeter of 176 , find the dimension

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