English, asked by yashaswinichauhan02, 7 months ago

the altitude of a right triangle is 7cm less than it's base. if the hypotenuse is 13cm, find the other two sides


Answers

Answered by HarshadaPawar7
3

Answer:

answer is 5 cm of the altitude

Answered by Anonymous
189

Given:-

  • The height of the triangle is 7cm less than its base.
  • The Hypotenuse = 13cm

To Find:-

  • The quadratic equation to find the base of the triangle

Solution:-

  • Let the base of the triangle be x.In this question, we given that the height is 7cm less than the base.Then :-
  • Height of the triangle will be = (x - 7)

\small\underline{\pmb{\sf  By \: applying\:  Pythagoras \: Theorem:-}}

\sf \:  \:  \:  \:  \:  \:  \:    \pink{Base^2 + Height^2 = Hypotenuse^2}\\

\sf \:  \:  \:  \:  \:  \:  \:   : \implies x^2 + (x - 7)^2 = 13^2\\

\sf \:  \:  \:  \:  \:  \:  \:   : \implies  x^2 + (x)^2 -2(x)(7) + (7)^2 = 13^2\\

\sf\:  \:  \:  \:  \:  \:  \:   :  \implies x^2 + x^2  - 14x + 49 = 169\\

\sf \:  \:  \:  \:  \:  \:  \:   : \implies 2x^2  - 14x + 49 - 169 = 0\\

\sf\:  \:  \:  \:  \:  \:  \:   :  \implies 2x^2 - 14x  - 120 = 0\\

\sf \:  \:  \:  \:  \:  \:  \:   : \implies 2(x^2 - 7x  - 60) = 0\\

\sf \:  \:  \:  \:  \:  \:  \:   : \implies x^2 - 7x  - 60 = 0\\

\sf \:  \:  \:  \:  \:  \:  \:   : \implies x^2 - 7x  - 60 = 0\\

\sf \:  \:  \:  \:  \:  \:  \:   : \implies x^2 -12x +5x  - 60 = 0\\

\sf\:  \:  \:  \:  \:  \:  \:   :  \implies x(x-12)+5(x-12)\\

\sf \:  \:  \:  \:  \:  \:  \:   : \implies (x-12)(x+5) = 0\\

\sf \:  \:  \:  \:  \:  \:  \: \pink{  : \implies x = 12,-5 }\\

  • (As side can't be negative.)

Hence,

  • Base = (x) = 12 cm
  • Height = (x - 7) = 12 - 7 = 5cm

\\

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