Question

Which of the following lengths represent the sides of a right triangle? Select all that apply.

a. 9cm,12cm,16cm
b. 8cm,15cm,17cm
c. 10cm,24cm,28cm
d. 6cm,8cm,10cm

Answer 1

The right triangles are options b and d. The lengths 8cm, 15cm, and 17cm (option b) and 6cm, 8cm, and 10cm (option d) are the correct answers.

Step-by-step explanation:

We can apply the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

Let's analyze each option:

a. 9cm, 12cm, 16cm:

To check if this forms a right triangle, we apply the Pythagorean Theorem:

9^2 + 12^2 = 81 + 144 = 225

16^2 = 256

Here, 225 is not equal to 256, so this set of lengths does not form a right triangle.

b. 8cm, 15cm, 17cm:

Applying the Pythagorean Theorem:

8^2 + 15^2 = 64 + 225 = 289

17^2 = 289

In this case, the sum of the squares of the two shorter sides is equal to the square of the longest side (hypotenuse), so this set of lengths represents a right triangle.

c. 10cm, 24cm, 28cm:

Using the Pythagorean Theorem:

10^2 + 24^2 = 100 + 576 = 676

28^2 = 784

Here, 676 is not equal to 784, so this set of lengths does not form a right triangle.

d. 6cm, 8cm, 10cm:

Applying the Pythagorean Theorem:

6^2 + 8^2 = 36 + 64 = 100

10^2 = 100

In this case, the sum of the squares of the two shorter sides equals the square of the longest side, so this set of lengths represents a right triangle.

Answer 2

Only the sets b (8cm,15cm,17cm) and d (6cm,8cm,10cm) represent the sides of a right triangle as they satisfy the Pythagorean theorem, where the sum of the squares of the two shorter sides equals the square of the longest side.

Step-by-step explanation:

The student is asking which of the following lengths represent the sides of a right triangle: 9cm,12cm,16cm; 8cm,15cm,17cm; 10cm,24cm,28cm; 6cm,8cm,10cm. To determine if the given lengths can form a right triangle, we can apply the Pythagorean theorem which states that in a right triangle, the sum of the squares of the legs (a and b) is equal to the square of the hypotenuse (c). In other words, a² + b² = c².

1. For set a (9cm,12cm,16cm), 9² + 12² = 81 + 144 = 225, which does not equal 16² (256), so this set does not form a right triangle.
2. For set b (8cm,15cm,17cm), 8² + 15² = 64 + 225 = 289, which is equal to 17² (289), so this set does form a right triangle.
3. For set c (10cm,24cm,28cm), 10² + 24² = 100 + 576 = 676, which does not equal 28² (784), so this set does not form a right triangle.
4. For set d (6cm,8cm,10cm), 6² + 8² = 36 + 64 = 100, which is equal to 10² (100), so this set does form a right triangle.

Thus, the sets of lengths that do represent the sides of a right triangle are b (8cm,15cm,17cm) and d (6cm,8cm,10cm).