Maths-
General
Easy

Question


In the figure above,  is parallel to . What is the length of  ?

hintHint:

Hint:
  • When two triangles are similar then their corresponding sides are proportional.
  • Pythagoras' theorem states that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

The correct answer is: Hence, The length of the side (CE) ⃗ is (CE) ⃗=30.


    Explanation:
    • In the given figure we have stack B D with rightwards arrow on top is parallel to stack A E with rightwards arrow on top , and the length of stack C B with rightwards arrow on top comma stack D B with rightwards arrow on top comma stack A E with rightwards arrow on top are 8 comma 6 comma 18 .
    • We have to find the length of stack C E with rightwards arrow on top .
    • We will apply the similarity properties of the triangle to find the length of stack C E with rightwards arrow on top .
    Step 1 of 1:


    In the given figure stack B D with rightwards arrow on top is parallel to stack A E with rightwards arrow on top
    So,
    text  In  end text straight triangle C B D text  and  end text subscript straight triangle C A E
    straight angle C B D equals straight angle C A E equals 90 to the power of ring operator
    straight angle C D B equals straight angle C E A
    straight angle D C B equals straight angle E C A
    So, Using A A A the two triangles straight triangle C B D and straight triangle C A E  are similar
    Step 2 of 2:
    Therefore,
    fraction numerator C B over denominator C A end fraction equals fraction numerator D B over denominator A E end fraction
    fraction numerator 8 over denominator C A end fraction equals 6 over 18
    C A equals 24
    Now Using Pythagoras theorem, in blank subscript straight triangle C A E end subscript
    We get
    C E squared equals C A squared plus A E squared
    C E squared equals 24 squared plus 18 squared
    C E squared equals 576 plus 324
    C E squared equals 900
    C E equals 30
    Final answer:
    Hence, The length of the side  stack C E with rightwards arrow on top text  is  end text stack C E with rightwards arrow on top equals 30 .

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