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Chapter 5: Q13 (page 180)

AE↔,BF↔,CG↔and DH↔are parallel, with EF=FG=GH. Complete.

If AC=22−x and BD=3x−22 then x= ? .

Short Answer

Expert verified

The length of x is 11 units.

Step by step solution

01

Step 1. Consider the diagram.

The parallel lines are shown as:

AE, BF, CG and DH are parallel to each other and EF=FG=GH. Length of AC and BD are 22−x and3x−22 respectively.

02

Step 2. Show the calculation.

Here, ADHE is the trapezoid as AE is parallel to DH.

As EF=FG=GH and AE, BF, CG and DH are parallel to each other, then, the lines BF and CG are the midsegment of the trapezoid.

Hence,

AB=BC=CD

The length of AC is:

AC=AB+BC=BC+BC

Then,

AC=2BC …… (1)

The length of BD is:

BD=BC+CD=BC+BC

Then,

BD=2BC …… (2)

From equations (1) and (2), the length AC is equal to BD.

The length of x is calculated as follows:

AB=BD22−x=3x−224x=44x=11

Thus, the length of x is 11 units.

03

Step 3. State the conclusion.

Therefore, the length of x is 11 units.

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