Respuesta :
Let b be the base and h be the height
h = 2 + 4b
area = 10
[tex]\text{Area of a triangle = }\frac{1}{2}\times b\times h[/tex][tex]10=\frac{1}{2}\times b\times(2+4b)[/tex][tex]10=\frac{b(2+4b)}{2}[/tex]Multiply bothside by 2
[tex]20=b(2+4b)[/tex][tex]20=2b+4b^2[/tex][tex]4b^2+2b\text{ - 20 =0}[/tex]Using factorization method to solve the above
Find two numbers such that its sum give 2 and its product gives -80
The two numbers are 10 and -8
Replace 2 by 10 and -8 in the expresion
[tex]4b^2+\text{ 10b-8b -20 = 0}[/tex][tex]2b(2b+\text{ 5) - 4(2b+}5)=0[/tex][tex](2b+5)(2b-4)=0[/tex]2b + 5 = 0 or 2b - 4 =0
2b = -5
b = -5/2 or 2b = 4
b = 2
since there is no negative length, then base is 2 feet
To get the height, substitute h = 2 + 4b
h = 2+ 4(2)
= 2 + 8
= 10
Height is 10 feet
The dimensions of the triangle is;
height = 10 feet
base = 2 feet
