Question

1. which right triangle has a hypotenuse that is greater than 13 feet long? 8.gr.1.1

a
11.2 ft
6.6 ft
b
9.6 ft
2.8 ft
c
14.4 ft
c
4.2 ft
d
12.6 ft
3.2 ft

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \( c = \sqrt{a^{2}+b^{2}} \), where \( a \) and \( b \) are the legs, and \( c \) is the hypotenuse. We need to calculate the hypotenuse for each option and check if it's greater than 13.

Step2: Calculate hypotenuse for Option A

\( a = 11.2 \), \( b = 6.6 \)
\( c = \sqrt{11.2^{2}+6.6^{2}}=\sqrt{125.44 + 43.56}=\sqrt{169}=13 \)
Not greater than 13.

Step3: Calculate hypotenuse for Option B

\( a = 9.6 \), \( b = 2.8 \)
\( c=\sqrt{9.6^{2}+2.8^{2}}=\sqrt{92.16+7.84}=\sqrt{100}=10 \)
Less than 13.

Step4: Calculate hypotenuse for Option C

\( a = 14.4 \), \( b = 4.2 \)
\( c=\sqrt{14.4^{2}+4.2^{2}}=\sqrt{207.36 + 17.64}=\sqrt{225}=15 \)
Greater than 13.

Step5: Calculate hypotenuse for Option D (optional, but for completeness)

\( a = 12.6 \), \( b = 3.2 \)
\( c=\sqrt{12.6^{2}+3.2^{2}}=\sqrt{158.76+10.24}=\sqrt{169}=13 \)
Not greater than 13.

Answer:

C. The right triangle with legs 14.4 ft and 4.2 ft (since its hypotenuse is 15 ft, which is greater than 13 ft)