Question

drag each triangle to the correct category.
for each set of side lengths, classify the triangle based on whether it is a right triangle.
4,4,√24 4,4,√32 7,8,15 8,7,√113 4,10,11
right triangle not a right triangle
reset next

Explanation:

To determine if a triangle is a right triangle, we use the Pythagorean theorem, \(a^2 + b^2 = c^2\), where \(c\) is the longest side.

Step 1: Analyze \(4, 4, \sqrt{24}\)

Longest side: \(\sqrt{24}\)
\(4^2 + 4^2 = 16 + 16 = 32\)
\((\sqrt{24})^2 = 24\)
\(32
eq 24\), so not a right triangle.

Step 2: Analyze \(4, 4, \sqrt{32}\)

Longest side: \(\sqrt{32}\)
\(4^2 + 4^2 = 16 + 16 = 32\)
\((\sqrt{32})^2 = 32\)
\(32 = 32\), so right triangle.

Step 3: Analyze \(7, 8, 15\)

Longest side: \(15\)
\(7^2 + 8^2 = 49 + 64 = 113\)
\(15^2 = 225\)
\(113
eq 225\), so not a right triangle.

Step 4: Analyze \(8, 7, \sqrt{113}\)

Longest side: \(\sqrt{113}\)
\(7^2 + 8^2 = 49 + 64 = 113\)
\((\sqrt{113})^2 = 113\)
\(113 = 113\), so right triangle.

Step 5: Analyze \(4, 10, 11\)

Longest side: \(11\)
\(4^2 + 10^2 = 16 + 100 = 116\)
\(11^2 = 121\)
\(116
eq 121\), so not a right triangle.

Answer:

Right Triangle: \(4, 4, \sqrt{32}\); \(8, 7, \sqrt{113}\)
Not a Right Triangle: \(4, 4, \sqrt{24}\); \(7, 8, 15\); \(4, 10, 11\)