Question

A square stained glass window is divided into four congruent triangular sections by iron edging to represent the seasons of the year. Each diagonal of the square window measures 9 inches.
What is the approximate total length of iron edging needed to create the square frame and the two diagonals?

43.5 inches
50.9 inches
54.0 inches
61.5 inches

Answer 1

Answer:

Option A

Step-by-step explanation:

Given that a square stained glass window is divided into four congruent triangular sections by iron edging to represent the seasons of the year

Each diagonal = 9 inches

Using Pythagorean theorem for right triangle with two sides and one diagonal we get

$9^2 = 2s^2\\s=\frac{9}{\sqrt{2} } =4.5(0.707)\\=6.363$

Iron rods needed for square with two diagonals

= perimeter of square + length of 2 diagonals

=4s+2d

=4(6.363)+2(9)

=43.452

Rounding off gives

43.5 inches Option A

Answer 2

Using the pythagoras theorem if the length of each side of the square is x:
2x^2 = 9^2 = 81
x = sqrt40.5 = 6.364 in

so  the total of iron strip needed = 4*6.364 + 2*9 =  43.5 ins  to nearest tenth