Respuesta :
Answer:
B
Step-by-step explanation:
Pythagorean theorem (applicable on right triangles only) says:
[tex]a^{2}+b^{2}=c^{2}[/tex]
- Where [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle and [tex]c[/tex] 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.
A.
[tex]8^{2}+12^{2}\\=64+144\\=208[/tex]
[tex]15^2=225[/tex]
They're not right triangle.
B.
[tex]10^{2}+24^{2}\\=100+576\\=676[/tex]
[tex]26^2=676[/tex]
This is a right triangle.
C.
[tex]12^{2}+20^{2}\\=144+400\\=544[/tex]
[tex]25^2=625[/tex]
They're not right triangle.
D.
[tex]15^{2}+18^{2}\\=225+324\\=549[/tex]
[tex]20^2=400[/tex]
They're not right triangle.
Only B is the right triangle.
The correct option is [tex]\boxed{{\mathbf{Option B}}}[/tex] .
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,
[tex]{H^2}={P^2}+{B^2}[/tex]
Here, [tex]H[/tex] is the hypotenuse, [tex]B[/tex] is the base and [tex]P[/tex] is the perpendicular.
Step by step explanation:
Step 1:
Option A: [tex]8,12,15[/tex]
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.
[tex]\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}[/tex]
It can be seen that the resultant length of the hypotenuse is [tex]\sqrt{208}[/tex] but the given hypotenuse s 15.
Therefore, the length of sides [tex]8,12,15[/tex] are not of right angle triangle as it does not satisfy the Pythagoras theorem.
Thus, option A is not correct.
Step 2:
Option B: [tex]10,24,26[/tex]
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.
[tex]\begin{gathered}{H^2}={10^2}+{24^2}\hfill\\{H^2}=100+576\hfill\\H=\sqrt{676}\hfill\\H=26\hfill\\\end{gathered}[/tex]
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 [tex]10,24,26[/tex] are of right angle triangle as it satisfies the Pythagoras theorem.
Thus, option B is correct.
Step 3:
Option C: [tex]12,20,25[/tex]
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.
[tex]\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}[/tex]
It can be seen that the resultant length of the hypotenuse is [tex]\sqrt{544}[/tex] but the given hypotenuse s 25.
Therefore, the length of sides [tex]12,20,25[/tex] are not of right angle triangle as it does not satisfy the Pythagoras theorem.
Thus, option C is not correct.
Step 4:
Option D: [tex]15,18,20[/tex]
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.
[tex]\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}[/tex]
It can be seen that the resultant length of the hypotenuse is [tex]\sqrt{549}[/tex] but the given hypotenuse s 20.
Therefore, the length of sides [tex]15,18,20[/tex] 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 https://brainly.com/question/839014
- 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? https://brainly.com/question/4419078
- Learn more about midpoint of the segment https://brainly.com/question/3269852
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.
