Question

algebra quadrilateral abcd is a rectangle.

1. if ( ac = 2x + 13 ) and ( db = 4x - 1 ), find db.
2. if ( ae = 3x + 3 ) and ( ec = 5x - 15 ), find ac.

3 if ( de = 6x - 7 ) and ( ae = 4x + 9 ), find db.

1. if ( mangle dac = 2x + 4 ) and ( mangle bac = 3x + 1 ), find ( mangle bac ).
2. if ( mangle abd = 7x - 31 ) and ( mangle cdb = 4x + 5 ), find ( mangle abd ).
3. if ( mangle bac = x + 3 ) and ( mangle cad = x + 15 ), find ( mangle bac ).

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal. So \(AC = DB\). Given \(AC=2x + 13\) and \(DB = 4x-1\), we set up the equation \(2x+13=4x - 1\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(13=2x - 1\). Then add \(1\) to both sides: \(14 = 2x\). Divide both sides by \(2\), we get \(x = 7\).

Step3: Find the value of \(DB\)

Substitute \(x = 7\) into the formula for \(DB\). Since \(DB=4x-1\), then \(DB=4\times7-1=28 - 1=27\).

Answer:

\(DB = 27\)