If the diagonal of a rectangle is 47 cm long and its perimeter is 96 cm. Find the area of the rectangle in sq. cm.

Answer 1

47.5 sq.cm

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Sides = x and y
Diagonal = SQRT(x^2+y^2)=47 ---> (1)
Perimeter = 2*(x+y)=96 ---> x+y=48 (2)
Area= xy=?

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(1) --> x^2+y^2=47^2=2209
(2) --> (x+y)^2=48^2 --> x^2+y^2 +2xy=2304--> considering (1) 2209 + 2xy=2304 --> xy=(2304-2209)/2= 47.5 sq.cm