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Chapter 5: Q16 (page 181)

In Exercises 16-17 a segment joins the midpoints of two sides of a triangle.

Find the values of x and y.

Short Answer

Expert verified

The length of x and y is 3 units and 3 units respectively.

Step by step solution

01

Step 1. Consider the diagram.

The triangle is shown below:

The line segment joins the midpoints of the triangle sides. Length of sides are 4y+2and 7y鈭�1. Length of midsegment and base of the triangle are 3x+5 and 12x鈭�8 respectively.

02

Step 2. Show the calculation.

Line segment passes through the midpoint of the side of the triangle.

Hence,

4y+2=7y鈭�14y+2=7y鈭�73y=9y=3units

According to the midsegment theorem, the length of the midsegment is half of the base of the triangle.

Hence,

3x+5=1212x鈭�83x+5=6x鈭�43x=9x=3units

Thus, the length of x is 3 units and y is 3 units.

03

Step 3. State the conclusion.

Therefore, the length of x and y is 3 units and 3 units respectively.

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