Lines AC¯¯¯¯¯¯¯¯AC¯ and BD¯¯¯¯¯¯¯¯BD¯ are diagonals of ABCDABCD . What value of x makes ABCDABCD a rectangle if AC=x+7AC=x+7 and BD=3x−5BD=3x−5 ?

Answer 1

A rectangle has opposite sides that are equal in length. Therefore, we can set the lengths of AC and BD equal to each other:

x + 7 = 3x - 5

Simplifying the equation:

2x = 12

Dividing by 2:

x = 6

Therefore, the value of x that makes ABCD a rectangle is 6.