. Geometry The area of a triangular sign is 33 square meters. The base of the triangle is 1 meter less than double the altitude. Find the altitude and the base of the sign.

Accepted Solution

Answer: The altitude and the base of the sign are 6 meters and 11 meters respectively.Step-by-step explanation:Since we have given that Area of triangular sign = 33 sq. metersLet the altitude of the triangle be 'x'.Let the base of the triangle be ' 2x-1'.As we know the formula for "Area of triangle ":[tex]Area=\dfrac{1}{2}\times base\times height\\\\33=\dfrac{1}{2}\times x(2x-1)\\\\33\times 2=2x^2-x\\\\66=2x^2-x\\\\2x^2-x-66=0\\\\2x^2-12x+11x-66=0\\\\2x(x-6)+11(x-6)=0\\\\(2x+11)(x-6)=0\\\\x=-\dfrac{11}{2},6\\\\x=-5.5,6[/tex]Discarded the negative value of x for dimensions:So, altitude of triangle becomes 6 metersBase of triangle would be [tex]2(6)-1=12-1=11\ meters[/tex]