Question

aiden calculated the area of triangle qrs by finding half the product of 1.5 and 1.1. what error did aiden make? aiden should have found half the product of 1.5 and 5.4 because the 1.1 line is a dotted line and not part of the figure. aiden should have found half the product of 1.5 and 1.2 because the 1.1 line is not perpendicular to the 1.5 line. aiden should have found half the product of 1.1 and 1.2 because the 1.5 line is not a dotted line in the figure. aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to the 1.1 line.

Explanation:

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\), where the base and height must be perpendicular to each other. In triangle \(QRS\), the side of length \(1.5\) (side \(QR\)) and the height of \(1.2\) (the dotted - line perpendicular to the other dotted - line) are not a base - height pair. The side of length \(1.5\) (side \(QR\)) and the height of \(1.1\) (the solid - line perpendicular to \(QS\)) are also not a base - height pair. The correct base - height pairs could be \(QS=(0.9 + 4.5)=5.4\) and height \(1.1\) or other valid perpendicular pairs. But analyzing Aiden's error: the key is that for the formula \(A = \frac{1}{2}\times base\times height\), the base and height must be perpendicular. The \(1.1\) line (height) is perpendicular to \(QS\) (not \(QR = 1.5\)).

Answer:

Aiden should have found half the product of \(1.1\) and \(5.4\) because the \(1.5\) line is not perpendicular to the \(1.1\) line.