Question

the hypotenuse of a right triangle is 6M more than twice the shortest side. if the third side is 2 metre less than the hypotenuse find the sides of a triangle.

Answer 1

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Here is your answer.
Let the Shortest side is x m

Hypotenuse =( 2x + 6)m

Third side is 2x + 6 - 2
= 2x + 4 m

ATQ
$(2x + 6) {}^{2} = {x}^{2} + (2x + 4) {}^{2} \\ \\ 4 {x}^{2} + 36 + 24x = {x}^{2} + 4 {x}^{2} + 16 + 16x \\ \\ {x}^{2} + 16x - 24x + 16 - 36 = 0 \\ \\ {x}^{2} - 8x - 20 = 0 \\ \\ {x}^{2} - 10x + 2x - 20 = 0 \\ \\ x(x - 10) + 2(x - 10) = 0 \\ \\ (x - 10)(x + 2) = 0 \\ \\ x = 10 \: \: and \: \: - 2 \\ \\ as \: number \: is \: not \: negative \: hence \\ \\ x = 10$
So
Shortest side is 10 m

Hypotenuse is 2×10 + 6 =26 m

Third side is 2×10 + 4 = 24 m


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Answer 2

$\huge{\boxed{\mathbb{ANSWER}}}$

QUADRATIC EQUATION PROBLEM SOLVING!

TO FIND : The all sides of a triangle.

Let us assume that the length of the shortest side be "x" meters

Hypotenuse = ( 2x + 6 ) metres

The third side of the triangle = ( 2x + 6 - 2 ) metres

= ( 2x + 4 ) meters

Now solving it by pythagoras theorem, we have :-

( 2x + 6 )² = x² + ( 2x + 4 )²

x² - 8x - 20 = 0

x² - 10x - 2x - 20 = 0

( x - 10 ) ( x + 2 ) = 0

x = 10 or , x = -2

( side of the triangle never in  negative )

so, x = 10

LENGTH OF THE SHORTEST SIDE = 10 metres

LENGTH OF THE HYPOTENUSE = ( 2x + 6 ) meters = 26m ( put

                                                                                  the value of x )

                                                                                                 

  LENGTH OF THE THIRD SIDE = 24 metres

ATLAST, I AM CONCLUDING MY WHOLE ANSWER :-

$\implies\boxed{\mathsf{The\:sides\:of\:the\:triangle\:are\:10metres,\:26metres\:and\:24metres.\:}}$