Mathematics, 20.08.2019 20:00 ritchieandrew249

Which set of numbers can represent the side lengths, in centimeters, of a right triangle?
a. 8,12,15
b. 10,24,26
c. 12,20,25
d. 15,18,20

Answers: 2

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Answers

For right angle triangles, we can apply pythagora's theorem, which states that the square of the longest side, the hypotenuse, is equivalent to the sum of the squares of the other two sides; mathematically this is: c^2 = a^2 + b^2. We check to see which one of the options satisfy this equation, taking the longes side to be c. In the case of B, 26^2 = 676 and 10^2 + 24^2 = 676, so B is the answer.

Answer from: yayrocks2395

The correct option is $\boxed{{\mathbf{option B}}}$ .

Further explanation:

Pythagoras theorem is used in a right angle triangle to find one of the side of the triangle.

The longest side in the right angle triangle is the hypotenuse.

Pythagoras theorem can be expressed as,

${H^2}={P^2}+{B^2}$

Here, is the hypotenuse, is the base and is the perpendicular.

Step by step explanation:

Step 1:

Option A: 8,12,15

The longest side is 15.

Therefore, consider 15 as hypotenuse and the remaining sides are perpendicular and base.

Now apply the Pythagoras theorem and substitute the value of perpendicular and base.

$\begin{gathered}{H^2}={P^2}+{B^2}\hfill\\{H^2}={12^2}+{8^2}\hfill\\{H^2}=144+64\hfill\\H=\sqrt{208}\hfill\\\end{gathered}$

It can be seen that the length of the hypotenuse is $\sqrt{208}$ but we have given 15.

Therefore, the given length of sides is not of right angle triangle as it does not satisfy the Pythagoras theorem.

Thus, option A is not correct.

Step 2:

Option B: 10,24,26

The longest side is 26.

Therefore, consider 26 as hypotenuse and the remaining sides are perpendicular and base.

Now apply the Pythagoras theorem and substitute the value of perpendicular and base.

$\begin{gathered}{H^2}={10^2}+{24^2}\hfill\\{H^2}=100+576\hfill\\H=\sqrt{676}\hfill\\H=26\hfill\\\end{gathered}$

It can be seen that the length of the hypotenuse is and we also have given 26.

Therefore, the given length of sides is of right angle triangle as it satisfies the Pythagoras theorem.

Thus, option B is correct.

Step 3:

Option C: 12,20,25

The longest side is 25.

Therefore, consider 25 as hypotenuse and the remaining sides are perpendicular and base.

Now apply the Pythagoras theorem and substitute the value of perpendicular and base.

$\begin{gathered}{H^2}={P^2}+{B^2}\hfill\\{H^2}={12^2}+{20^2}\hfill\\{H^2}=144+400\hfill\\H=\sqrt{544}\hfill\\\end{gathered}$

It can be seen that the length of the hypotenuse is $\sqrt{544}$ but we have given 25.

Therefore, the given length of sides is not of right angle triangle as it does not satisfy the Pythagoras theorem.

Thus, option C is not correct.

Step 4:

Option D: 15,18,20

The longest side is 20.

Therefore, consider 20 as hypotenuse and the remaining sides are perpendicular and base.

Now apply the Pythagoras theorem and substitute the value of perpendicular and base.

$\begin{gathered}{H^2}={P^2}+{B^2}\hfill\\{H^2}={15^2}+{18^2}\hfill\\{H^2}=225+324\hfill\\H=\sqrt{549}\hfill\\\end{gathered}$

It can be seen that the length of the hypotenuse is $\sqrt{549}$ but we have given 20.

Therefore, the given length of sides is not of right angle triangle as it does not satisfy the Pythagoras theorem.

Thus, option D is not correct.

Learn more:

Learn more about the all right triangles are isosceles link Learn more about in a right triangle, angle c measures 40°. the hypotenuse of the triangle is 10 inches long. what is the approximate length of the side adjacent to angle c? link Learn more about the distance between the points link

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Triangles

Keywords: side, lengths, distance, Pythagoras theorem, triangle, hypotenuse, base, perpendicular, right angle triangle, longest side, equation, satisfy, centimeters.

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