Question

7. Given the area of the non-shaded region is 315 square feet, find the base and height of the large triangle X + 6 2x +2 3x + 5 + Base= feet Height = feet

Answer 1

Step-by-step explanation:

The height of the triangle is

`2x+2+x+6=3x+8`

the base length is

`2(3x+5+3)=6x+16`

Therefore, the area of the larger triangle is

`Area=(6x+16)(3x+8)`

Similarly, the area of the shaded triangle is

`(x+6)(3x+5)`

Therefore, the area of the unshaded region is

`(6x+16)(3x+8)-(x+6)(3x+5)`

which simplifies to give

`15x^2+73x+98`

and we know that the area of the unshaded region is 315 and so

`15x^2+73x+98=315`

which simplifies to give

`15x^2+73x-217=0`

and the solution to the equation is

`x=2.082`

With the value of x in hand, we now find the base and height lengths.

`\begin{gathered} height=3x+8=3(2.082)+8 \\ \boxed{height=14.246} \end{gathered}`

and

`\begin{gathered} base=6x+16=2(2.082)+16 \\ \boxed{base=20.164} \end{gathered}`

Hence,

height = 14. 246

base = 20.164