Question

in the triangle xyz, lm is the mid segment. find the length of yz. 4.9 cmoptions: 4.2 cm, 9.8 cm, 5.8 cm, 11.8 cm

Explanation:

Step1: Recall Midsegment Theorem

The Midsegment Theorem states that the midsegment of a triangle is parallel to the third side and half as long as the third side. So, \( LM=\frac{1}{2}YZ \).

Step2: Solve for \( YZ \)

Given \( LM = 4.9 \, \text{cm} \), we can rearrange the formula to find \( YZ \). Multiply both sides of the equation \( LM=\frac{1}{2}YZ \) by 2: \( YZ = 2\times LM \). Substitute \( LM = 4.9 \, \text{cm} \) into the formula: \( YZ=2\times4.9 = 9.8 \, \text{cm} \).

Answer:

9.8 cm (corresponding to the option "9.8 cm")