Question

Answer by true or false and justify your answer in both cases.

Given: e = (7 – 0.5)² = 1. The scientific notation of e is 1.69.
A = 832x is a rational number.
Given ANP is an equilateral triangle, such that AN = √52 – 3²cm, then the length of the height (AH) relative to (NP) is √3 cm.

Answer 1

The length of the height relative to NP in an equilateral triangle is half of the length of one of the sides, not sqrt(3) cm.

Step-by-step explanation:

The given statement is: Given ANP is an equilateral triangle, such that AN = √52 – 3²cm, then the length of the height (AH) relative to (NP) is √3 cm.

To determine if this statement is true or false, we need to calculate the value of AN using the given expression and then find the length of the height relative to NP.

AN = √52 – 3² = √25 – 9 = √16 = 4 cm.

In an equilateral triangle, the height (AH) divides the base (NP) into two equal parts. Since the length of ANP is 4 cm and ANP is an equilateral triangle, the length of the height (AH) relative to NP is half of AN, which is 2 cm, not √3 cm. Therefore, the given statement is false.