Question

ABCD is a rectangle. Find the length of each diagonal. AC=3y/5 BD=3y-4

Answer 1

Since a rectangle the diagonals AC and BD are congruent. 3y/5 = 3y-4. 3y =15y -20. y=5y-20 -4y=-20 y=5

Answer 2

The diagonals of a rectangle are equal, so

$\frac{3y}{5} = 3y-4$, then multiply both sides by 5
3y = 5(3y - 4) Distribute the 5
3y = 15y - 20 Subtract 15y from both sides
-12y = -20 Divide both sides by -12
y = $\frac{5}{3}$

So, AC = $\frac{3(5/3)}{5} = 1$
and BD = 3(5/3) - 4 = 1