Question

(1.) This is a blueprint drawing of the stage area at Millennium Park. The length of one square on the grid is equal to 5 feet. According to the blueprint, the length of the diagonal of square C is 60 feet. Is that correct? Explain. (2.) If the blueprint is drawn on the coordinate plane with vertices (1, 5) and (11, 15) for the corners labeled with red stars, would that be an accurate representation of the length of the diagonal of the square C? Show your work and explain your reasoning.

Answer 1

Let's begin by listing out the information given to us:

One square grid = 5 feet

The side of the square measures 10 grids = 5 * 10 = 50 feet

Squares have all sides congruent. This means that both the length & width of the square equals 50 feet

To obtain the length of the diagonal of the square, we will calculate using Pythagoras Theorem as shown below:

c² = a² + b²

a = 50 ft, b = 50 ft, c = ?

c² = 50² + 50² = 2500 + 2500 = 5000

c² = 5000 ⇒ c = 70.7

c = 70.7 ft

The length of the diagonal according to the plan is not 60 feet. Hence, it is wrong