Question

ABCD is a rectangle. Find the length of each diagonal.

AC = 2 (5a + 1)
BD = 2(a + 1)

Answer 1

In a rectangle diagonals is equal (|AC| = |BD|), therefore

2(5a + 1) = 2(a + 1) |divide both sides by 2

5a + 1 = a + 1 |subtract 1 from both sides

5a = a |subtract "a" from both sides

4a = 0 |divide both sides by 4

a = 0

subtitute to 2(a + 1)

|AC| = |BD| = 2(0 + 1) = 2(1) = 2

Answer 2

`2(5a+1)=2(a+1)\\ 10a+2=2a+2\\ 8a=0\\ a=0\\\\ 2\cdot(0+1)=2\cdot 1=2`

It's 2.