Question

Two adjacent sides of a parallelogram have length of 5 cm and 11 cm. Each of the two diagonals divide the parallelogram into two congruent triangles. If the lengths of the diagonals are the smallest and the greatest possible prime values (as sides of the triangles), then what is the sum of the lengths of the diagonals ?

Answer 1

20 cm

Explanation:

Since the diagonals have to be prime numbers, and they have to be able to be sides of a triangle, the formula would be 6<x<16. The prime numbers in this group are 7, 11, and 13. Since 7 is the smallest prime number in this group and 13 is the largest, 7+13=20.