We can cancel the 1/2 by multiplying by 2: 88*2 = (1/2)(h+5)(h)*2 176 = (h+5)(h)
Using the distributive property, we have: 176 = h² + 5h
We want quadratic equations to be set equal to 0, so we will subtract 176 from both sides: 176 - 176 = h² + 5h - 176 0 = h² + 5h - 176
Using the quadratic formula: [tex]h=\frac{-b\pm \sqrt{b^2-4ac}}{2a}
\\
=\frac{-5\pm \sqrt{5^2-4(1)(-176)}}{2(1)}=\frac{-5\pm \sqrt{25--704}}{2}
\\
\\=\frac{-5\pm \sqrt{25+704}}{2}=\frac{-5\pm \sqrt{729}}{2}
\\
\\=\frac{-5\pm 27}{2}=\frac{-5-27}{2}\text{ or }\frac{-5+27}{2}
\\
\\=\frac{-32}{2}\text{ or }\frac{22}{2}=-16\text{ or }11[/tex]
Since a negative length makes no sense, we know that h=11.
The base is 5 inches longer than the height, so b = 11+5 = 16.
