Math, asked by zaib118, 8 months ago

the altitude of a right triangle is 7 cm less than its base if the hypo is 13 cm find the other 2 sides​

Answers

Answered by TBNRAnirudh
1

Answer:

12 cm and 5 cm

Step-by-step explanation:

Answered by BlessedMess
22

Given,

  • Altitude of right triangle is 7 cm less than its base.
  • Hypotenuse is 13 cm.

To find,

  • The other two sides.

Solution,

Let x be the base of the triangle

Then altitude will be (x-7)

We know that,

\sf{Base^2+Altitude^2=Hypotenuse^2}

So, by pythagoras theorem,

 {x}^{2}   +  ( {x - 7)}^{2}  =  {13}^{2}  \\ \\  ⟹2 {x}^{2} -  14x + 49  = 169 \\ \\   ⟹2 {x}^{2}  - 14x + 49 - 169 = 0  \\ \\  ⟹2 {x}^{2}  - 14x - 120 = 0 \\ \\  ⟹2( {x}^{2}  - 7x - 60) = 0 \\ \\  ⟹ {x}^{2}  - 7x - 60 =  \frac{0}{2}  \\  \\⟹ {x }^{2}  - 7x - 60 = 0 \\ \\  ⟹  {x}^{2}  - 12x + 5x - 60 = 0 \\ \\  ⟹x(x - 12) + 5(x - 12) = 0 \\  \\ ⟹(x - 12)(x + 5) = 0

So, x = 12 or x = -5

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

And the altitude will be (12-7) = 5 cm

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