Question

A triangle has two sides of length 15 cm and 17 cm. Select all the values of its third side that would make it a right triangle

A: 8cm

B: 29 cm

C: 2 cm

D: 514 radical cm

E: 29 radical cm

Answer 1

the answer is A.

Explanation:

For a right triangle one can find the length of the longest side by using the Pythagorean theorem. So there are two options I can think of that if the triangle is a right triangle will work. First remember what the Pythagorean theorem is : side a^2+side b^2=hypotenuse^2

The hypotenuse is the longest side of a right triangle. So if the sides that are 15 and 17 cm are not the longest sides.

Answer 2

`√(514) cm`, 8cm, are both options

Explanation:

For a right triangle one can find the length of the longest side by using the Pythagorean theorem. So there are two options I can think of that if the triangle is a right triangle will work. First remember what the Pythagorean theorem is : side a^2+side b^2=hypotenuse^2

The hypotenuse is the longest side of a right triangle. So if the sides that are 15 and 17 cm are not the longest sides then the formula would be:

`15^(2) +17^2=c^2\\15^2+17^2=√(514)cm`

But if 17cm is the longest side then:

`a^2+15^2=17^2\\8^2+15^2=17^2\\a=8cm`

Hope this helps!