Question

Which real-world scenario involves a right triangle?
A. a triangular bathroom tile with side lengths of 6 inches, 8 inches, and 12 inches
B. a triangular bike path with lengths of 5 miles, 12 miles, and 13 miles
C. a triangular plot of land with side lengths of 10 yards, 10 yards, and 15 yards
D. a triangular street sign with side lengths of 3 feet, 3 feet, and 3 feet

Answer 1

B . because it satisfies the theory

Answer 2

Answer:

A triangular plot of land with side lengths of 10 yards, 10 yards, and 15 yards is not a  real-world scenario involves a right triangle.

Step-by-step explanation:

A. a triangular bathroom tile with side lengths of 6 inches, 8 inches, and 12 inches:

• Let it be a real-world scenario involves a right triangle with three sides x, y, and z , where z is the hypotenuse.

• Now, according to Pythagorean theorem $x^{2}$+$y^{2}$ = $z^{2}$

• now, $6^{2}$ + $8^{2}$ = 36 + 64 = 100 = $10^{2}$ ≠ $12^{2}$

• So, we can conclude that , a triangular bathroom tile with side lengths of 6 inches, 8 inches, and 12 inches is not a  real-world scenario involves a right triangle.

B. a triangular bike path with lengths of 5 miles, 12 miles, and 13 miles:

• Let it be a real-world scenario involves a right triangle with three sides x, y, and z , where z is the hypotenuse.

• Now, according to Pythagorean theorem $x^{2}$+$y^{2}$ = $z^{2}$

• now, $5^{2}$ + $12^{2}$ = 25 +144 = 169 = $13^{2}$
• So, we can conclude that , a triangular bike path with lengths of 5 miles, 12 miles, and 13 miles , is a  real-world scenario involves a right triangle.

C. a triangular plot of land with side lengths of 10 yards, 10 yards, and 15 yards:

• Let it be a real-world scenario involves a right triangle with three sides x, y, and z , where z is the hypotenuse.

• Now, according to Pythagorean theorem $x^{2}$+$y^{2}$ = $z^{2}$

• now, $10^{2}$ + $10^{2}$ = 100 + 100 = 200  ≠ $15^{2}$
• So, we can conclude that, a triangular plot of land with side lengths of 10 yards, 10 yards, and 15 yards is not a  real-world scenario involves a right triangle.

D. a triangular street sign with side lengths of 3 feet, 3 feet, and 3 feet.

• Let it be a real-world scenario involves a right triangle with three sides x, y, and z , where z is the hypotenuse.

• Now, according to Pythagorean theorem $x^{2}$+$y^{2}$ = $z^{2}$

• now, $3^{2}$ + $3^{2}$ = 9 + 9 = 18  ≠ $3^{2}$
• So, we can conclude that, a triangular street sign with side lengths of 3 feet, 3 feet, and 3 feet is not a  real-world scenario involves a right triangle.

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