Question

Question #7922f

Answer 1

Yes

Explanation:

Using Pythagorus

For a right angled triangle `h^2 = a^2 + b^2` where `h` is the hypotenuse and `a` and `b` are the other two sides

conversely if the sum of the squares of `a` and `b` = the square of the hypotenuse, then the triangle must be right-angled.

Substitute in what we know
`15^2 = 9^2 + 12^2`

Simplify
`225 = 81 + 144 = 225`

Therefore the triangle is a right-angled triangle

Answer 2

`"right triangle"`

Explanation:

`"using the "color(blue)"converse theorem of Pythagoras"`

`"if the longest side squared is equal to the sum of the "`
`"other two sides squared then it is a right triangle"`

`rArr15^5=225larrcolor(blue)"longest side squared"`

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

`"since "15^2=9^2+12^2`

`"then it is a right triangle"`