how do u solve this geometry question to solve hj=5x jk=7x kh=96?
To solve this geometry question, you can use the properties of triangles and their interior angles. Let's break down the problem step by step:
1. Start by drawing a diagram of the triangle with the given side lengths. Label the vertices as H, J, and K, and mark the side lengths as HJ = 5x, JK = 7x, and KH = 96.
2. Remember that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we have HJ + JK > KH, JK + KH > HJ, and KH + HJ > JK.
3. Apply these inequalities to the given side lengths and simplify the expressions:
- 5x + 7x > 96 (HJ + JK > KH)
- 12x > 96
- x > 8
- 7x + 96 > 5x (JK + KH > HJ)
- 2x > -96
- x > -48
- 96 + 5x > 7x (KH + HJ > JK)
- -2x > -96
- x < 48 (Note the direction of the inequality changes when multiplying/dividing by a negative number.)
4. Based on the inequalities, we can conclude that x lies between -48 and 48, excluding the endpoints.
Therefore, the solution to the geometry question is: -48 < x < 48.