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15 November, 22:05

31. ABCD has area equal to 28 sq. unit. BC is parallel to AD and BA perpendicular to AD. If BC = 6 and AD = 8,

then value of CD =

B. 213

A. 2 12

C. 4

D. 275

+1
Answers (1)
  1. 15 November, 22:10
    0
    The value of CD is 2√5

    Step-by-step explanation:

    * Lets describe the figure to know its name

    - ABCD is a quadrilateral

    ∵ BC parallel to AD

    ∵ BC = 6 units and AD = 8 units

    - The quadrilateral which has two parallel sides not equal in length is a

    trapezoid

    ∴ ABCD is a trapezoid, where BC and AD are its bases

    ∵ BA perpendicular to AD

    ∴ BA is the height of the trapezoid

    - The area of the trapezoid = 1/2 (base 1 + base 2) * its height

    ∵ The bases of the trapezoid are BC and AD

    ∵ BC = 6 and AD = 8

    ∵ Its area = 28 units²

    ∴ 1/2 (6 + 8) * height = 28

    ∴ 1/2 (14) * height = 28

    ∴ 7 * height = 28 ⇒ divide both sides by 7

    ∴ height = 4

    ∵ The height is BA

    ∴ BA = 4 unit

    - To find the length of CD draw a perpendicular line from C to AD and

    meet it at E

    ∵ BA and CE are perpendicular to AD

    ∴ BA / / CE

    ∵ BC / / AD

    - Perpendicular lines between parallel lines are equal in lengths

    ∴ BA = CE and BC = AE

    ∵ BA = 4 and BC = 6

    ∴ CE = 4 and AE = 6

    ∵ AD = 8 units

    ∵ AD = AE + ED

    ∴ 8 = 6 + ED ⇒ subtract 6 from both sides

    ∴ ED = 2 units

    - In ΔCED

    ∵ m∠CED = 90°

    ∴ CD = √[ (CE) ² + (ED) ²] ⇒ Pythagoras theorem

    ∵ CE = 4 and ED = 2

    ∴ CD = √[ (4) ² + (2) ²] = √[16 + 4] = √20 = 2√5

    * The value of CD is 2√5
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