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Chapter 5: Q27 (page 170)

鈻�DECKis a parallelogram. Complete.

Ifm鈭�1=3x,m鈭�2=4x and m鈭�3=x2-70then x=?andm鈭�CED=? (numerical answers).

Short Answer

Expert verified

The value of x and鈭�CED is 10 and 70掳respectively.

Step by step solution

01

Step 1. Apply property of parallelogram.

Alternate interior angles of a parallelogram are equal.

From the figure, it can be observed that,

3x=x2鈭�70x2鈭�3x鈭�70=0;4x=鈭�DEK

02

Step 2. Description of step.

Solve the obtained quadratic equation in step 1 to find the value of x.

x2鈭�3x鈭�70=0x2鈭�10x+7x鈭�70=0xx鈭�10+7x鈭�10=0x鈭�10=0orx+7=0x=10orx=-7

03

Step 3. Solve the quadratic equation.

Solving equation x2鈭�3x鈭�70=0gives the roots as, x=10;x=鈭�7

Only positive values are to be considered, therefore the acceptable value of x is 10.

04

Step 4. Solve the quadratic equation.

鈭�CEDcan be expressed as 鈭�CED=鈭�DEK+x2鈭�70.

Substitute 4x for 鈭�DEKinto 鈭�CED=鈭�DEK+x2鈭�70.

鈭�CED=4x+x2鈭�70

05

Step 5. Description of step.

Substitute 10 for x into 鈭�CED=4x+x2鈭�70.

鈭�CED=410+102鈭�70=40+100鈭�70=70掳

Therefore, the value of x and鈭�CED is 10 and 70掳respectively.

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