Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

The base of a right triangle is four more than three times the height. If the hypotenuse is five times the...?

height find how high the triangle is (the height)

5 Answers

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  • ?
    Lv 7
    2 months ago

    Let a=the base; b=the height; c=the hypotenuse. It follows that

    a^2+b^2=c^2

    =>

    (3b+4)^2+b^2=(5b)^2

    =>

    9b^2+24b+16+b^2=25b^2

    =>

    15b^2-24b-16=0

    =>

    b=2.106 or b=-0.506 (rejected)

    =>

    the height=2.106 approximately.

  • Pope
    Lv 7
    2 months ago

    The more obvious case has already been covered, but there is another solution, equally valid and quite a bit simpler.

    Do you understand that any side of a triangle may be identified as the base? Let the hypotenuse be the base. The height then is the altitude from the angle opposite the hypotenuse. The fact that it is a right triangle is of no matter, but does no harm.

    Let the height be h.

    (hypotenuse) = 4 + 3h

    (hypotenuse) = 5h

    5h = 4 + 3h

    2h = 4

    h = 2

    The height of the triangle is 2.

  • 2 months ago

    Refer to the following figure :

    According to the question --

    ( 3 h + 4 )² + h²  = ( 5 h )² ................. Using Pythagoras theorem.

     ( 3 h + 4 )² = ( 5 h )² -  h² 

    => (3h+4)²  =  24 h²   ........ Take squire root of both the sides.

    => 3 h + 4  =  ± 2√6 h  .................. 

    We will, now, calculate h  considering firstly +ve and again considering (-)ve sign.

    (1) Positive sign :  3 h + 4  =  + 2√6 h  

    =>  h (2√6 - 3)  =  4  ====>>>>  h  =  4/(2√6 - 3) =  2.27

    (2) Negative sign. :  3 h + 4  =  -  2√6 h 

    =>  3 h +  2√6 h  =  - 4  =====>>>>  h = -ve value.... to be neglected.

    Hence  h  =  2.27  ........... Answer

    Attachment image
  • 2 months ago

    The base of a right triangle is 4 more than 3 times the height. 

    If the hypotenuse is 5 times the height find how high the triangle is (the height)

    h^2 + (3h + 4)^2 = (5h)^2

    10h^2 + 24h + 16 = 25h^2

    15h^2 - 24h - 16 = 0

    75/128 (h - 4/5)^2 = 1

    Solutions:

    h = 4/5 - (8 sqrt(2/3))/5 ≈ -0.50639

    h = 4/5 + (8 sqrt(2/3))/5 ≈ 2.1064      ====> Answer

     

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  • ted s
    Lv 7
    2 months ago

    the reference triangle is { 3h + 4 , h , 5h }.....thus (5h)² = h² + ( 3h + 4)² ===> √24  h = 3 h + 4 ===> h = 4 / [ - 3 + √24 ]

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