Question

The height and sides of a triangle are four consecutive integers. the height is the first integer, and the base is the third integer. The perimeter of the triangle is 42 in. Find the area of the triangle.

Answer 1

84 in²

Explanation:

The side lengths of the triangle are 3 consecutive integers whose sum (the perimeter) is 42. The average of those integers, 42/3 = 14, is the middle of the three, so they are 13, 14, 15. We're told the perimeter is in inches, so all of these dimensions are inches.

These are the last three of 4 consecutive integers, so the first, the height of the triangle, is 12. The base of the triangle is the 3rd of the four integers, so is 14. Then the area is ...

A = (1/2)bh = (1/2)(14)(12) = 84 . . . . . square inches.