If the diagonal of a rectangle is 23 cm long and its perimeter is 52 cm. Find the area of the rectangle in sq. cm.

Answer 1

73.5 sq. cm

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Sides = x and y
Diagonal = SQRT(x^2+y^2)=23 ---> (1)
Perimeter = 2*(x+y)=52 ---> x+y=26 (2)
Area= xy=?

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(1) --> x^2+y^2=23^2=529
(2) --> (x+y)^2=26^2 --> x^2+y^2 +2xy=676 --> considering (1) 529 + 2xy=676 --> xy=(676-529)/2=73.5