# Find each side of a quadrilateral if its perimeter is 54 cm and the sides are 3: 4: 5: 6.

August 30, 2021 | education

| Given:

ABCD – rectangle,

AB / BC / CD / DA = 3/4/5/6,

P avcd = 54 centimeters.

Find the lengths of the sides of the rectangle: AB, BC, CD, DА -?

Solution:

1) Consider a rectangle ABCD. Let the length of the side AB = 3 * x centimeters, the length of the side BC = 4 * x centimeters, the length of the side CD = 5 * x centimeters, the length of the side DA = 6 * x centimeters. We know that the perimeter of the rectangle is 54 centimeters. Then

3 * x + 4 * x + 5 * x + 6 * x = 54;

18 * x = 54;

x = 54: 18;

x = 3;

2) 3 * 3 = 9 centimeters – AB;

3) 4 * 3 = 12 centimeters – BC;

4) 5 * 3 = 15 centimeters – CD;

5) 6 * 3 = 18 centimeters – DA.

Answer: 9 centimeters; 12 centimeters; 15 centimeters; 18 centimeters.