Question

pythagorean theorem converse hw1.2b
#7. tina built a triangular sign with side lengths of 73 inches, 55 inches and 4 feet. is the sign a right triangle? why or why not?
a yes; because 73² + 48² = 55². 4 feet is equal to 48 inches
b no; because 4² + 55² ≠ 73². 4² is too small of a side to form a right triangle.
c no; because 48² + 55² = 5329. the hypotenuse must be 5329 inches.
d yes; because 48² + 55² = 73². 4 feet is equal to 48 inches

Explanation:

Step1: Convert 4 feet to inches

Since 1 foot = 12 inches, 4 feet = 4×12 = 48 inches.

Step2: Apply Pythagorean theorem converse

The Pythagorean theorem converse states that for side - lengths \(a\), \(b\), and \(c\) of a triangle (\(c\) being the longest side), if \(a^{2}+b^{2}=c^{2}\), then the triangle is a right - triangle. Here, \(a = 48\), \(b = 55\), and \(c = 73\). Calculate \(a^{2}+b^{2}\): \(48^{2}+55^{2}=2304 + 3025=5329\), and \(73^{2}=5329\). Since \(48^{2}+55^{2}=73^{2}\), the triangle is a right - triangle.

Answer:

D. Yes; because \(48^{2}+55^{2}=73^{2}\). 4 feet is equal to 48 inches