For going to a city B ...

 For going to a city B from city A, there is a route via city C such that AC 

perpendicular to CB, Ac = 2 x km and CB = 2(x + 7) km. It is proposed to 

construct a 26 km highway which directly connects the two cities A and B. Find 

how much distance will be saved in reaching city B from city A after the 

construction of the highway

Comments

  1. UnknownNovember 30, 2020 at 9:46 AM

    By using pythagorus theorem in the triangle formed by the given detaiswe get that x= 5 so
    AC = 10 km and BC = 24 km
    so total distance from City A to city B = 24+10 = 34 km
    Hence , the distance saved is = 34-26=8km

    ReplyDelete
  2. AnonymousDecember 1, 2020 at 1:57 PM

    26 km becomes the hypotenuse while the base and the perpendicular become 2(x+7) and 2x respectively and the triangle is right angled at C.
    Using Pythagoras theorem we get the equation 26^2=(2x)^2 +(2x+14)^2 which can be simplified into 0= x^2 +7x -60 so we get x=5 or -12 and -12 gets neglected so x=5.

    Hence the base becomes 2((5)+7)=24 km
    The perpendicular = 2(5) = 10 km
    Hence the route through AB BC is 10+24=34 km

    Distance between A and B through highway is 26 km
    By going through the route AB then BC is 34 km
    Hence the distance saved = 34 km-26 km=8 km

    Hence 8 km is saved by the construction of the highway.

    ~By Kriishh Gada

    ReplyDelete
  3. UnknownDecember 1, 2020 at 3:09 PM

    On using Pythagoras theorem , we get the quadratic equation x^2 + 7x - 60 = 0.On solving this equation we get x= 5 or x= -12, but length cannot be -ve so x=5.

    Hence, we get AC=10 km , BC= 24 km and AB=26 km. On using through AB and BC the total distance is 34 km. But the highway is of length 26 km.

    Therefore, length of 8 km is saved in travelling from city A to city B.

    -By Somil Kashyap

    ReplyDelete
  4. Deepti HajelaDecember 1, 2020 at 9:12 PM

    Well done Somil.

    ReplyDelete
  5. Deepti HajelaDecember 1, 2020 at 9:13 PM

    Kriishh Gada- Good!

    ReplyDelete
  6. Sanjam BediDecember 2, 2020 at 9:27 AM

    In right angle triangle at C, 26 km becomes the hypotenuse while the base and the perpendicular become 2(x+7) and 2x respectively .
    Using Pythagoras theorem we get the equation 26^2=(2x)^2 +(2x+14)^2 which can be reduced to 0= x^2 +7x -60 so we get x=5 or -12.
    But length cannot be in negative, so x=5

    Hence :
    AC-10km
    BC-24km
    AB-26km

    Distance through AB and Bc is 34 km. But the length of highway is 26 km.
    Distance saved is =34-26
    = 8km

    Hence 8 km will be saved after the construction of the highway.

    Sanjam Bedi
    10-B


    ReplyDelete
  7. Deepti HajelaDecember 2, 2020 at 9:59 PM

    Correct Sanjam!

    ReplyDelete
  8. UnknownDecember 28, 2020 at 6:52 PM

    On using pythagoras theorem in right angled triangle ABC , we get a quadratic eq. - x^2 + 7x - 60 = 0. On solving it we get x= 5 ( x=-12 is not possible since x is distance and hence can't be negative ) ... By substituting the value of x we get
    AC=10km , BC=24km, AB=26km

    Distance saved =( AC + BC ) - AB
    = 34 - 26
    = 8 Km

    Therefore 8 Km will be saved after the construction of highway

    - Mital Amit Tripathi
    Class 10 F

    ReplyDelete

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