Question

1. a triangle has a perimeter of 90 cm and a very small area. what might be its height? p=90cm s₁=s₂=s₃=30cm

Explanation:

Step1: Analyze Triangle Type

The triangle has equal sides (\(s_1 = s_2 = s_3\)), so it's equilateral. Perimeter \(P = 90\) cm, so side length \(s=\frac{90}{3}=30\) cm.

Step2: Relate Area and Height

For a triangle with very small area, the height must be small. In an equilateral triangle, height \(h = \sqrt{s^2 - (\frac{s}{2})^2}=\sqrt{30^2 - 15^2}=\sqrt{675}\approx25.98\) cm for a regular equilateral triangle. But if the area is very small, the triangle is "flat" (almost degenerate), so height approaches 0. A possible small height (e.g., 1 cm, 2 cm, etc.) works. Let's take a very small value, say \(h \approx 1\) cm (or any small positive number, as the problem asks "what might be its height" for a very small area, so a small height like a few centimeters is reasonable).

Answer:

A very small height, e.g., \(\boldsymbol{1}\) cm (or other small positive values like 2 cm, 0.5 cm, etc., as the triangle is nearly degenerate for very small area).