Mathematics, 12.10.2019 11:50 laskew37221

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

Answers: 3

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Answers

Answer from: marfeliz5953

Step-by-step explanation:

Pythagorean theorem (applicable on right triangles only) says:

$a^{2}+b^{2}=c^{2}$

Where

and

are the two legs of the triangle and

is the length of the hypotenuse [THE LONGEST SIDE].

We can square each leg on the triangle and take the sum, if that is equal to the square of the longest side, we have a right triangle. Let's check for all of these.

$8^{2}+12^{2}\\=64+144\\=208$

15^2=225

They're not right triangle.

$10^{2}+24^{2}\\=100+576\\=676$

26^2=676

This is a right triangle.

$12^{2}+20^{2}\\=144+400\\=544$

25^2=625

They're not right triangle.

$15^{2}+18^{2}\\=225+324\\=549$

20^2=400

They're not right triangle.

Only B is the right triangle.

Answer from: mcaninch36

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

Further explanation:

Pythagoras theorem is applied in a right angle triangle to obtain one of the side of the triangle.

The longest side of the right angle triangle known as hypotenuse.

Pythagoras theorem can be written 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

In the above option the longest side is 15.

Then, consider 15 as hypotenuse and 12, 8 are perpendicular and base respectively.

Now use the Pythagoras theorem and then substitute the value of given 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 resultant length of the hypotenuse is $\sqrt{208}$ but the given hypotenuse s 15.

Therefore, the length of sides 8,12,15 are 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

In the above option the longest side is 26.

Then, consider 26 as hypotenuse and 10, 24 are perpendicular and base respectively.

Now use the Pythagoras theorem and then substitute the value of given 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 resultant length of the hypotenuse is 26 and the given hypotenuse is also 26.

Therefore, the length of sides 10,24,26 are of right angle triangle as it satisfies the Pythagoras theorem.

Thus, option B is correct.

Step 3:

Option C: 12,20,25

In the above option the longest side is 25.

Then, consider 25 as hypotenuse and 12, 20 are perpendicular and base respectively.

Now use the Pythagoras theorem and then substitute the value of given 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 resultant length of the hypotenuse is $\sqrt{544}$ but the given hypotenuse s 25.

Therefore, the length of sides 12,20,25 are 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

In the above option the longest side is 20.

Then, consider 20 as hypotenuse and 15, 18 are perpendicular and base respectively.

Now use the Pythagoras theorem and then substitute the value of given 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 resultant length of the hypotenuse is $\sqrt{549}$ but the given hypotenuse s 20.

Therefore, the length of sides 15,18,20 are 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 midpoint of the segment 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.

Answer from: Quest

Ithink it’s b, hope this .

Answer from: Quest

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3 x =27

8)17.80