Determine whether the following triangles are right.
We test if the above is a right triangle by plugging the side lengths into the Pythagorean Theorem and checking if the resulting statement is true. That is to say if:
AB^{2} + AC^{2}= BC^{2}
Here we have:
- BC=9
- AB=4
- AC=6
On the one hand:
AB^{2} + AC^{2}= 4^2+6^2=16+36=52
On the other hand:
BC^{2}=9^2=81
We observe that:
AB^{2} + AC^{2}\neq BC^{2}
This is not a right triangle.
We test if the above is a right triangle by plugging the side lengths into the Pythagorean Theorem and checking if the resulting statement is true. That is to say if:
AB^{2} + AC^{2}= BC^{2}
Here we have:
- AB=3
- BC=4
- AC=5
On the one hand:
AB^{2} + BC^{2}= 3^2+4^2=9+16=25
On the other hand:
AC^{2}=5^2=25
We observe that:
AB^{2} + BC^{2}=AC^{2}
This is a right triangle.
We test if the above is a right triangle by plugging the side lengths into the Pythagorean Theorem and checking if the resulting statement is true. That is to say if:
AB^{2} + AC^{2}= BC^{2}
Here we have:
- AB=2
- BC=4
- AC=6
On the one hand:
AB^{2} + BC^{2}= 2^2+4^2=4+16=20
On the other hand:
AC^{2}=6^2=36
We observe that:
AB^{2} + BC^{2}\neq AC^{2}
This is not a right triangle.
We test if the above is a right triangle by plugging the side lengths into the Pythagorean Theorem and checking if the resulting statement is true. That is to say if:
AC^{2} + BC^{2}= AB^{2}
Here we have:
- AC=7
- BC=24
- AB=25
On the one hand:
AC^{2} + BC^{2}= 7^2+24^2=49+576=625
On the other hand:
AB^{2}=25^2=625
We observe that:
AC^{2} + BC^{2}= AB^{2}
This is a right triangle.
We test if the above is a right triangle by plugging the side lengths into the Pythagorean Theorem and checking if the resulting statement is true. That is to say if:
AB^{2} + BC^{2}= AC^{2}
Here we have:
- AB=13
- BC=5
- AC=14
On the one hand:
AB^{2} + BC^{2}= 13^2+5^2=169+25=194
On the other hand:
AC^{2}=14^2=196
We observe that:
AB^{2} + BC^{2}\neq AC^{2}
This is not a right triangle.
We test if the above is a right triangle by plugging the side lengths into the Pythagorean Theorem and checking if the resulting statement is true. That is to say if:
AB^{2} + AC^{2}= BC^{2}
Here we have:
- BC=6
- AB=5
- AC=\sqrt{11}
On the one hand:
AB^{2} + AC^{2}= 5^2+\sqrt{11}^2=25+11=36
On the other hand:
BC^{2}=6^2=36
We observe that:
AB^{2} + AC^{2}= BC^{2}
This is a right triangle.
We test if the above is a right triangle by plugging the side lengths into the Pythagorean Theorem and checking if the resulting statement is true. That is to say if:
AB^{2} + BC^{2}= AC^{2}
Here we have:
- AB=4
- BC=4
- AC=7
On the one hand:
AB^{2} + BC^{2}= 4^2+4^2=16+16=32
On the other hand:
AC^{2}=7^2=49
We observe that:
AB^{2} + BC^{2}\neq AC^{2}
This is not a right triangle.