Answer:
height = 8 in
width = 22 in
Step-by-step explanation:
Let x inches be the height of the triangle.
The width of a triangle is six more than twice the height, then the width of the triangle is [tex]2x+6[/tex] inches.
The area of the triangle is [tex]88\ in^2.[/tex]
Use formula
[tex]A_{\triangle}=\dfrac{1}{2}\cdot \text{Width}\cdot \text{Height}[/tex]
to find x:
[tex]88=\dfrac{1}{2}\cdot (2x+6)\cdot x\\ \\88=(x+3)x\\ \\x^2+3x-88=0\\ \\D=3^2-4\cdot (-88)=9+352=361=19^2\\ \\x_{1,2}=\dfrac{-3\pm \sqrt{361}}{2}=\dfrac{-3\pm 19}{2}=-11,\ 8[/tex]
The height cannot be negative, so
height = 8 in
width = 22 in
