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
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
Answer:
The correct answer is 43.44 inches.
Step-by-step 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
\(x^2+x^2=9^2\)
\(x=\frac{9}{\sqrt{2}}=6.36 inches\)
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.