Question

In square SLIM, SI and LM intersect at T. If LT=4x-1 and MT =3x+1 , what is the length of LT

Answer 1

The length of LT in square SLIM is 7 units, determined by setting the expressions for LT and MT equal to each other and solving for x.

Step-by-step explanation:

In square SLIM, where SI and LM intersect at T, we are given the lengths of two segments in terms of x: LT is 4x-1 and MT is 3x+1. Since SLIM is a square, SI and LM are diagonals which bisect each other. This implies that LT equals MT because the diagonals of a square are congruent and bisect each other. To solve for the length of LT, we set 4x-1 equal to 3x+1 and solve for x.

Here is a step-by-step solution:

1. Write the equation 4x-1 = 3x+1.
2. Subtract 3x from both sides to get x-1 = 1.
3. Add 1 to both sides to get x = 2.
4. Substitute the value of x back into the expression for LT, which is 4x-1.
5. Calculate LT by substituting x into the expression 4(2)-1 to get 8-1 = 7.

Therefore, the length of LT is 7 units.