Given that the area of the triangles is the sum of powers of the prime factors of the number 1628. Find the sum of areas of the triangles and find the number of triangles. [4 MARKS]

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Solution

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Prime factors of 1628 are

$1628 = 2^{2} \times 3 \times 7 \times 19$ .

Since thare are 5 prime factors,

$\Rightarrow$ The number of given triangles are = 5

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

$\Rightarrow$ The sum of areas of the triangle = 2 + 1 + 1 + 1

= 5 square units

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