Question

The area of a certain number of triangles is equal to the sum of the exponents of the prime factors of the number 1628, and each prime factor represents a triangle. Find the sum of areas of the triangles and find the number of the triangles.​

Answer 1

Given that,

The area of a certain number of triangles is equal to the exponents of the prime factors, of the number 1628 and each prime factor represent a triangle.

Prime factors of 1628 are:

1628= 2×2×3×7×19

Since there are 5nprime factors,

-> The number of given triangles are= 5

The area of the triangles is the sum of powers of the prime factors.

-> The sum of areas of triangle= 2+1+1+1

= 5 square unit

The number of triangles is 5 and the sum of areas of the triangles is 5 square units.