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

21/2 or 5/2

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)