Describe the possible side lengths of the 3rd side of the triangle given the lengths of the 2 other sides? 9 inches, 8 inches explain! you. : )

Heya !

Using a theoram about triangles ,

Given a triangle ∆ABC, the sum of the lengths of any two sides of the triangle is greater than the length of the third side ,

Also , the length of third side always greater than absolute difference of the other two sides ,

Let the third side be x ,

So , x < 9 + 8 and x > 9 - 8
x < 17 and x > 1

Hence , x ∈ [ 2 , 17 ] inch.

Above case is true for any triangle , be it scalene , Isosceles , Right-angled ...

As , for Isosceles , the third side can be 8 or 9 inches ,
For scalene , all values in the above range satusfies ,

For right angled triangle , we have 2 cases ,

Case 1 : Third side is the hypotenuse
Then , x = √(9²+8²) = √145 = 12.0415 inch.

Case 2 : Third side is not the hypotenuse
Then , x = √(9²-8²) = √17 = 4.1231 inch.

Hope it helps you ! :)

There are two possible choices for the third side. One is using the 9 as the hypotenuse, and the number less than 9. The second is using the number as they hypotenuse.
Remember to use the a² + b² = c² formula.

let the hypotenuse side be "x".

9² + 8² = x²
Simplify
81 + 64 = x²
Add
x² = 145
Root both sides
√x² = √145
Answer
x = 12.04159 (rounded)

let one of the sides (not hypotenuse) be x

9²- 8² = x²
Simplify
81 - 64 = x²
Subtract
x² = 17
Root both sides to isolate the x
√x² = √17
Answer
x = 4.12310 (rounded)

hope this helps

The academic affairs council is the highest expert body processing academic affairs, as stipulated by the university statutes. specialist aaro häkkinen (educational policy) took part in the council’s meeting. the agenda of the meeting included bachelors’ feedback, the timing of pedagogical studies, the grant system for tuition fees, the standardisation of administrative practices for internships and the situation of foreign-language and multilingual master’s programmes.

Ineed on quadratic equations to solve problems