SOLUTION: if the area of rectangle is 168 centimetres square and its diagonal is 25 centimetre find its length breath and perimeter

Question 924783: if the area of rectangle is 168 centimetres square and its diagonal is 25 centimetre find its length breath and perimeter
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let l be the length of rectangle and w be the width, then we have two equations
l * w = 168
l^2 + w^2 = 25^2
solve first equation for l
l = 168 / w
substitute for l in second equation
(168/w)^2 +w^2 = 25^2
(28224/w^2 +w^2 = 625
multiply both sides of = by w^2
28224 +w^4 = 625w^2
w^4 -625w^2 +28224 = 0
this equation has the following solution set
w = (-24, -7, 24, 7)
we are only interested in positive values of w and in a rectangle l > w
so we pick w = 7 cm and l is 24 cm
check answer
24^2 + 7^2 = 25^2
576 + 49 = 625
625 = 625
answer checks

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