Question

the flower garden has the shape of triangle 34ft of a perrenial border forms the hypotenuse of the triangle and one leg is 14 ft longer than the other leg. find the length of the legs

Answer 1

The setup for this problem is a triangle that is (x+14)-(x)-34. I am assuming this is a right triangle since no angles are given.
\[(x+14)^{2}+x^{2}=34^{2}\]
Expanded:
\[x^2+28x+196+x^2=1156\]
Simplified:
\[2x^2+28x+196=1156\]
Set to 0:
\[2x^2+28x-960=0\]
Divide by 2 to make factoring easier:
\[x^2+14x-480=0\]
Factor:
\[(x+30)(x-16)=0\]
Therefore:
\[x=-30,16\]
Discard the negative value as side cannot be negative. Therefore the sides are:
30-16-34
Proof:
\[30^2+16^2=34^2\]
\[900+256=1156\]