Mathematics
Grade9
Easy

Question

In the given figure, DE || BC, and all measurements are in centimeters. The length of AC is

  1. 5 cm
  2. 4.5 cm
  3. 5.25 cm
  4. 5.5 cm

hintHint:

Prove the triangles are similar and if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

The correct answer is: 5.25 cm


    In ΔABC and ΔADE,
    angle A equals space angle A (common)
    angleADE = angleABC (Corresponding angles are equal)
    Therefore, By AA similarity 
    ΔABC ~ ΔADE 
    fraction numerator A D over denominator A B end fraction equals fraction numerator A E over denominator A C end fraction thin space left parenthesis c o r r e s p o n d i n g space s i d e s space a r e space i n space e q u a l space p r o p o r t i o n right parenthesis
l e t space A E space b e space x space t h e n space A C space equals space 3 space plus space x space
G i v e n comma space A D space equals space 3 space a n d space A B space equals space 3 plus space 4 space equals space 7
3 over 7 equals fraction numerator x over denominator x plus 3 end fraction
3 left parenthesis x space plus space 3 right parenthesis space equals space 7 x
9 space equals space 4 x
x space equals space 2.25
T h e r e f o r e comma space A C space equals space space x space plus space 3 space equals space 2.25 space plus space 3 space equals space 5.25 space
    Therefore, the length of AC is 5.25 .

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