Final answer:
The estimated length of the diagonal of a square with an area of 100 cm² is found by first determining the side length and then using the formula d = 1.4·(side length)⁻½, resulting in an estimated diagonal of approximately 14.1 cm.
Step-by-step explanation:
The question asks for the estimated length of the diagonal of a square with an area of 100 cm², using the formula d = 1.4x⁻½. To find the length of a square's diagonal when the area is known, we first need to determine the side length of the square. Since the area of a square is found using the formula side length squared, we can find the side length by taking the square root of the area. In this case, the side length is √(100 cm²) which equals 10 cm. We then apply the formula for the diagonal:
d = 1.4 × (side length)⁻½
By substituting in the side length (10 cm), we get:
d = 1.4 × (10 cm)⁻½ =
d = 1.4 × (10¹⁻½) =
d = 1.4 × 3.16 cm ≈ 14.1 cm
Hence, the answer is B. 14.1 cm.