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Arturo is building a flower bed in the shape of a right triangle. The hypotenuse of the right triangle is 13 feet. One of the legs needs to be 7 feet longer than the other leg. Which equation can be used to find x, the length of the shorter leg?

Respuesta :

kevinvarnell
x(x+7)=169 Hope this helps out :-)

Answer:  [tex]13^2=x^2+(x+7)^2[/tex] is used to find 'x'.

Step-by-step explanation:

Let the length of other leg be 'x'.

Since we have given that one of the legs needs to be 7 feet longer than the other leg.

So, Length of one leg = x+7

Hypotenuse of the right triangle = 13 feet.

Since it form right angle triangle.

so, we can use "Pythagorus theroem".

[tex]13^2=x^2+(x+7)^2\\\\169-(x+7)^2=x^2\\\\169-(x^2+49+14x)=x^2\\\\169-x^2-49-14x=x^2\\\\120-14x=2x^2\\\\60-7x=x^2\\\\x^2+7x-60=0\\\\x^2+12x-5x-60=0\\\\x(x+12)-5(x+12)=0\\\\(x+12)(x-5)=0\\\\x=5[/tex]

Hence, [tex]13^2=x^2+(x+7)^2[/tex] is used to find 'x'.

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