Question

kuta software - infinite pre - algebra
the pythagorean theorem
do the following lengths form a right triangle?
1)
3)

1. a = 6.4, b = 12, c = 12.2

find each missing length to the nearest tenth.
7)
9)
11)

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side).

Step2: Check problem 1

Let \(a = 6\), \(b = 8\), \(c = 9\). Calculate \(a^{2}+b^{2}=6^{2}+8^{2}=36 + 64=100\) and \(c^{2}=9^{2}=81\). Since \(100
eq81\), these lengths do not form a right - triangle.

Step3: Check problem 3

Let \(a = 6\), \(b = 8\), \(c = 10\). Calculate \(a^{2}+b^{2}=6^{2}+8^{2}=36 + 64 = 100\) and \(c^{2}=10^{2}=100\). Since \(a^{2}+b^{2}=c^{2}\), these lengths form a right - triangle.

Step4: Check problem 5

Let \(a = 6.4\), \(b = 12\), \(c = 12.2\). Calculate \(a^{2}+b^{2}=6.4^{2}+12^{2}=40.96+144 = 184.96\) and \(c^{2}=12.2^{2}=148.84\). Since \(184.96
eq148.84\), these lengths do not form a right - triangle.

Step5: Solve problem 7

Let the missing side be \(x\). Using \(a^{2}+b^{2}=c^{2}\), if \(a = 4\), \(c = 8\), then \(b=\sqrt{c^{2}-a^{2}}=\sqrt{8^{2}-4^{2}}=\sqrt{64 - 16}=\sqrt{48}\approx6.9\).

Answer:

1. No
2. Yes
3. No
4. Approximately \(6.9\)