Question 131462
For a triangle,
{{{A = (1/2)*b*h}}}
{{{A = 30}}} cm2
{{{h = b - 4}}} cm
{{{30 = (1/2)*b*(b - 4)}}}
multiply both sides by {{{2}}}
{{{60 = b^2 - 4b}}}
{{{b^2 - 4b - 60 = 0}}}
Complete the square
{{{b^2 - 4b + (4/2)^2 = 60 + (4/2)^2}}}
{{{(b - 2)^2 = 64}}}
{{{b - 2 = 8}}} (only the + square root makes sense here)
{{{b = 10}}}
{{{h = b - 4}}}
{{{h = 10 - 4}}}
{{{h = 6}}}
The base is 10 cm and the height is 6 cm
check:
{{{A = 30}}}
{{{A = (1/2)*b*h}}}
{{{30 = (1/2)*10*6}}}
{{{30 = 30}}}
OK