Answer
(A) a=25, b=60, c=39, d=52
(B) 1764 square units
Work Step by Step
A) We are asked to pick a combination of the given four lengths that makes the statement true. Thus, we need to pick the lengths such that the two sides of the equation result in the same value. We pick a=25, b=60, c=39, d=52. Checking this selection:
$$ a^2+b^2=c^2 + d^2 \\ 25^2 + 60^2 = 39^2 +52^2 \\ 4225 = 4225$$
We find the area using the equation for area:
$$ A = \frac{ab+cd}{2} \\ A =\frac{(25)(60)+(39)(52)}{2} \\ A = 1764 \ square \ units$$
