Question

In rectangle ABCD, AC = 7x - 15 and BD = 2x + 25.
Find the lengths of the diagonals of ABCD.

Answer 1

the length of ac is 75

The area of a rectangle is given as:
Area = Length x width
We have,
AC = 3x + 15
BD = 4x - 5
AC and BD are diagonals of the rectangle.
The diagonals of a rectangle are equal.
Now,
AC = BD
3x + 15 = 4x - 5
15 + 5 = 4x - 3x
20 = x
Now,
AC = 3x + 15
= 3 x 20 + 15
= 60 + 15
= 75
Thus,
AC = 75