Question

PLEASE HELP IM BEGGING Ira B. Scholar, that bizarre math teacher, put the figure at right on a recent test and said,

"If the perimeter is 25, solve for x." Show Ira B. that such a figure does not exist. Use algebra and
explain your result (why perimeter cannot equal 25).

Answer 1

The perimeter is the distance all the way around the outside of a 2D shape. To calculate the perimeter, sum the lengths of all the sides.

Therefore, perimeter of the triangle = (2x - 8) + (2x + 5) + (30 - 3x)

Collect like terms: 2x + 2x - 3x - 8 + 5 + 30

Combine like terms: x + 27

Therefore, perimeter of triangle = x + 27

We are told that the perimeter is 25:

x + 27 = 25

Subtract 27 from both sides: x = -2

If x = -2, then the side with equation 2x - 8 = (2 x -2) - 8 = -12

A length cannot be negative, therefore the perimeter cannot equal 25.