I need help with this math problem solving grade 11 question?
I have this bad in my test and I have to correct, but I'm not sure how do … This is the question: In a conservation park, a rescuer has used 620m of marker buoys to cordon off a pool safety are. If one side of the rectangular area is the beach, what is the largest area that can be included? What are the dimensions of the bathing area? Thanks:)
Draw a rectangle and the label of a pair of opposite sides as 'x' meters. 'x' represent the width of the defined area. In one of the remaining sides, labeled as "(620 – 2x) 'meters. This is due to the length of the 3 sides must be equal to 620m, as you describe. The area of a rectangle is given by length * width. So therefore: A = x (620 – 2x) A = 620x – 2x ^ 2 To find the maximum area, we must differentiate the area. Therefore: DA / dx = 620 – 4x The area is greatest when dA / dx = 0. Therefore: 620 – 4x = 0 620 = 4 x = 155m Therefore, the width is 155mm and length is: 620-2 (155) = 620 to 310 = 310m Therefore, the dimensions are 155m x 310m and the maximum area is 48050m ^ 2
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