In rectangle FGHJ FH 3x 9 and GJ 63 5x Find the value of

In rectangle FGHJ, FH = 3x - 9 and GJ = 63 - 5x. Find the value of x, and the lengths of the diagonals of FGHJ.

Solution

Since it has been given that the given figure is a rectangle, then by the property of the rectangle, the diagnols are equal.

Therefore 3x - 9 = 63 - 5x

Solving 8x = 72, therefore x = 9

Therefore the lengths of the diagnols FH = JG = 3x - 9 = 27-9 = 18 (similarly 63-5x is also equal to 18)