To calculate: The dimensions of a billboard when a rectangular billboard has a perimeter of 72 ft. and an area of 288 ft2.

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To calculate: The dimensions of a billboard when a rectangular billboard    has a perimeter of 72 ft. and an area of 288 ft2.

Fachur · Accepted Answer

Given Information:    A rectangular billboard has a perimeter of 72 ft. and an area of 288 ft2.  Formula used:    Consider x be length and y be breadth of a rectangle.    Perimeter of above rectangle is 2(x+y).    Area of above rectangle is xy    Calculation:    Let the length be x and the width be y.    It is provided that a rectangular billboard has a perimeter of 72 ft.    Put provided value of perimeter in above formula,    Therefore,    2x+2y=72    Divide both sides of the above equation by 2 and simplify,    2x+2y2=722    x+y=36    The rectangular billboard has an area of 288 ft2.    Put provided value of area in above formula,    Therefore,    xy=288    The system of equation becomes:    x+y=36………..(1)     xy=288………….(2)    Consider equayion (2)    xy=288     xy=288x    Substitute 288x for yin equation (1),    x+288x=36    x2+288=36x    x2−36x+288=0    Simplify further to obtain,    x2−36x+288=0     x2−24x−12x+288=0    x(x−24)−12(x−240)=0    V    Apply law of zero product,    Therefore,    x=24 or x=12    Substitute 24 for xin equation (2),    24y=288    y=12    Substitute 12 for xin equation (2),    12y=288    y=24    The solution set (24, 24) does not satisfy both the provided equations.    The solution set (24. 12) satisfies both the provided equations.    Therefore, the width of the rectangular billboard is 24 ft. and the length is 12 ft.

To calculate: The dimensions of a billboard when a rectangular billboa

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