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

Question

anonymous · Answer

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:
$$30^2+16^2=34^2$$
$$900+256=1156$$