The side lengths of a quadrilateral produce an arithmetic sequence. If the longest side has a length of 24 cm and the perimeter is 60 cm, what are the other side lengths? Explain your reasoning.



Answer :

Answer:

6cm, 12cm, 18cm

Step-by-step explanation:

Let the shortest side be "a" and the common difference will be "d"
Hence, the four sides form an arithmetic sequence: a, a + d, a + 2d, a + 3d because of a + (n-1)d

The sum of the four sides is the perimeter

a + (a + d) + (a + 2d) + (a + 3d) = 4a + 6d

4a + 6d = 60

2a + 3d = 30 (Equation 1)

The longest side, a + 3d, has a length of 24cm

a + 3d = 24 (Equation 2)

Solve simultaneously

2a + 3d = 30

- a + 3d = 24

a = 6

6 + 3d = 24

3d = 18

d = 6

The other side lengths are a, a+d, a+2d

= 6cm, 12cm, 18cm