Question

The area of a square is three times the area of a triangle. If the base of the triangle and a side of the square are equal, what is the ratio of the side of the square to the height of the triangle?

Answer 1

The area of a triangle with a base of 166 mm and a height of 930 mm is calculated using the formula A = 1/2 × base × height, resulting in the area in square meters of 0.0772 m² when rounded to three significant figures.

Step-by-step explanation:

The formula for finding the area of a triangle is A = 1/2 × base × height. To find the area of a triangle with a base of 166 mm and a height of 930 mm, we use this formula:

A = 1/2 × 166 mm × 930 mm

First, multiply the base and height: 166 mm × 930 mm = 154380 mm². Then divide by 2 to get the area:

A = 154380 mm² / 2

A = 77190 mm²

To express this in square meters, knowing that 1 mm² = 1×10⁻⁶ m², we get:

A = 77190 mm² × 1×10⁻⁶ m²/mm²

A = 0.077190 m²

Since we are looking for the answer in square meters and must express it to the proper number of significant figures, we consider the initial measurements, which are given to three and four significant figures respectively. Hence, our final answer, in accordance with the significant figures rules, should also have three significant figures.

A = 0.0772 m²