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The altitude of a right angle triangle is 7cm

2 thoughts on “{<br />\<br />[tex]{\red{\underline{\overline{ǫᴜᴇsᴛɪᴏɴ:-}}}}[/tex]<br /><br /><br />The altitude of a right angle triangle is 7cm”

1. Step-by-step explanation:

   base = x

   altitude = x – 7

   by Pythagoras theorem

   Base² + height² = hypotenuse ²

   [tex] { x}^{2} + {(x – 7)}^{2} = {13}^{2} \\ {x}^{2} + {x }^{2} – 14x + 49 = 169 \\ 2 {x }^{2} – 14x + 49 – 169 = 0 \\ 2 {x}^{2} – 14x – 120= 0 [/tex]

   divide the above equation by 2 we get

   [tex] {x}^{2} – 7x – 60 = 0 \\ {x }^{2} – 12x + 5x – 60 = 0 \\ x(x – 12) + 5(x – 12) \\ = (x – 12)(x + 5) = 0 \\ x = 12 [/tex]

   since x= -5 is neglected as it is negative.

   [tex]base \: equals \: 12 \\ height \: equals \: x – 7 = 12 – 7 \\ = 5[/tex]

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2. Given:–

   • Hypotenuse = 13cm

   To Find:–

   • the other two sides of right-angled triangle.

   step-by-step solution:–

   Let x be the base of the triangle, then the altitude will be (x−7).

   By Pythagoras theorem,

   • → x² +(x−7)² = (13)²
   • → 2x² −14x + 49 − 169=0
   • → 2x² −14x−120 = 0
   • → x² − 7x − 60 = 0
   • → x² − 12x + 5x − 60 = 0
   • → (x − 12)(x + 5) = 0
   • → x = 12,x = −5

   Since the side of the triangle cannot be negative, so the base of the triangle is 12cm and,

   the altitude of the triangle will be 12−7 = 5cm.

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