Question

I’m confused on this one

Answer 1

The formula of an area of a triangle

$A=\dfrac{bh}{2}$

We have $b, h = b + 3, A = 35 ft^2$

Substitute:

$\dfrac{b(b+3)}{2}=35\ \ \ |\cdot2\\\\b^2+3b=70\ \ \ |-70\\\\b^2+3b-70=0\\\\b^2+10b-7b-70=0\\\\b(b+10)-7(b+10)=0\\\\(b+10)(b-7)=0\iff b+10=0\ \vee\ b-7=0\\\\b=-10 < 0\ \vee\ b=7$

The altitude $b+3=7+3=10\ ft$

Answer: 10ft.