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

The correct answer is 43.44 inches.

Explanation:

The diagonal of square = 9 inches

let the sides of the square be x

On applying Pythagoras theorem in Δ ABC

`AB^2+BC^2=AC^2`

AB = BC = x

`x^2+x^2=9^2`

`x=(9)/(√(2))=6.36 inches`

Diagonals of the square bisect each other.

OC = OA = 4.5 inches and OB = OD = 4.5 inches

Total length of iron edge required for window :

=4 × Length of square + 2 diagonals

= 4 × 6.36 + 2 × 9 = 43.44 inches

The closest answer from the given options is 43.44 inches.

Answer 2

Diagonal of the square (d):
d = a · √2 = a · 1.414 ( a is a length of a side of the square )
a = 9 : 1.414 = 6.365 inches
Total length:
4 · a + 2 · d = 4 · 6.365 + 2 · 9 = 25.46 + 18 = 43.46 ≈ 43.5 inches.
Answer: A ) 43.5