Question

PLEASE HELP!!!

A triangle has two sides that measure 6 inches and 26 inches. A similar triangle has sides that measure exactly half of the length of the original triangle. What is the greatest possible area of the smaller triangle?

Answer 1

19.5 in²

Explanation:

A applicable formula for the area of the smaller triangle is ...

A = (1/2)ab·sin(C) . . . . where a, b are the given sides and C is the angle between them.

The side lengths are 3 in and 13 in, so the area is ...

A = (1/2)(3 in)(13 in)sin(C) = (19.5 in²)sin(C)

The sine function is a maximum at C=90°, at which angle it has the value 1. So, the maximum area is that of a right triangle of sides lengths 3 and 13 inches.

The maximum area is 19.5 in².