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Chapter 5: Q4 (page 180)

Points A, B, E and F are midpoints of XC炉,XD炉,YC炉and YD炉. Complete.

If CD=8x, andAB=3x+2 then x= ? .

Short Answer

Expert verified

x=2

Step by step solution

01

Step 1. Consider the diagram.

Here, A, B, E and F are the midpoints of sides XC炉,XD炉,YC炉and YD炉respectively.

And CD=8xand AB=3x+2.

02

Step 2. Show the calculation.

Consider the triangle 鈻�XCD.

Here, points A and B are the midpoints of XC炉and XD炉.

So, by theorem 5-11 part (2), the side AB炉is half as long as the third side CD炉.

AB=12CD 鈥︹�� (1)

Substitute CD=8xand AB=3x+2.

AB=12CD3x+2=128x3x+2=4x2=4x鈭�3x2=x

03

Step 3. State the conclusion.

Therefore, x=2.

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