Answer:
Option (C)
Step-by-step explanation:
From the graph attached,
In ΔABC and ΔA'B'C',
∠A ≅ ∠A'
∠B ≅ ∠B'
Therefore, ΔABC ~ ΔA'B'C'
Corresponding sides of these triangles will be proportional.
Therefore, ratio of the sides, AC : A'C' = 1 : 3 shows that image triangle A'B'C' is a dilated form of pre-image ABC with a scale factor of 3.
Option (C) will be the correct option.
Length: 2w + 59
width: w
diagonal: (2w + 59) + 2 = 2w + 61
Length² + width² = diagonal²
(2w + 59)² + (w)² = (2w + 61)²
(4w² + 118w + 3481) + w² = 4w² + 122w + 3721
5w² + 118w + 3481 = 4w² + 122w + 3721
w² + 118w + 3481 = 122w + 3721
w² - 4w + 3481 = 3721
w² - 4w - 240 = 0
a = 1, b = -4, c = -240
w =
=
=
=
=
=
since width cannot be negative, disregard 1 - 2√61
w = 1 + 2√61 ≈ 16.62
Length: 2w + 59 = 2(1 + 2√61) + 59 = 2 + 4√61 + 59 = 61 + 4√61 ≈ 92.24
Answer: width = 16.62 in, length = 92.24 in