Question

8. A right triangle has a perimeter of 24 cm and a hypotenuse of 10 cm. Find the length of the other two sides.

Answer 1

You will need to make a system:
Draw your right triangle. The hypotenuse (length 10) is C. The two legs (the other sides) are A and B.
We know that A+B+C=24, so A+B=14
By the Pythagorean theorem, A^2 + B^2 = C^2, so A^2 + B^2 = 10^2 = 100
Solve the first equation for A: A = 14-B.
Now, we plug it in.
\[A^2+ B^2=100 \rightarrow (14-B)^2+B^2 = 100 \rightarrow (B^2-28B+196)+B^2=100\]
\[\rightarrow 2B^2-28B+196=100 \rightarrow B^2-14B+48=0 \rightarrow (B-8)(B-6)=0 \]
Solving for B, we find B= 8 or 6. If we plug these values into A+B=14, we find:
A=6 & B=8 OR A=8 & B=6. So, the two lengths are 6 and 8.

Answer 2

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