Question

20 mark for review the perimeter of an equilateral triangle is 624 centimeters. the height of this triangle is ( ksqrt{3} ) centimeters, where ( k ) is a constant. what is the value of ( k )?

Explanation:

Step1: Find side length of triangle

An equilateral triangle has 3 equal sides. Perimeter = 3×side. So side \( s=\frac{624}{3}=208 \) cm.

Step2: Derive height formula for equilateral triangle

For an equilateral triangle with side \( s \), height \( h \) splits it into two 30 - 60 - 90 triangles. The height \( h=\frac{\sqrt{3}}{2}s \).

Step3: Substitute side length into height formula

Substitute \( s = 208 \) into \( h=\frac{\sqrt{3}}{2}s \). So \( h=\frac{\sqrt{3}}{2}\times208 = 104\sqrt{3} \). Since \( h = k\sqrt{3} \), then \( k = 104 \).

Answer:

104