Question

The width of a triangle is six more than twice the height. The area of the triangle is 88in^2

Answer 1

height = 8 in

width = 22 in

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
`2x+6` inches.

The area of the triangle is
`88\ in^2.`

Use formula

`A_(\triangle)=(1)/(2)\cdot \text{Width}\cdot \text{Height}`

to find x:

`88=(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)=(-3\pm √(361))/(2)=(-3\pm 19)/(2)=-11,\ 8`

The height cannot be negative, so

height = 8 in

width = 22 in