Question 1021942

A square and a triangle have the same area. The base of the triangle is 3 ft. more than the side length of the square. The height of the triangle is 1 ft. less than the base of the triangle. What is the side length of the square? What are the base and height of the triangle?
<pre>Let the length of one side of the square, be S
Then area of square = {{{S^2}}}
Also, length of base of triangle = S + 3, and height = S + 3 – 1, or S + 2
Area of triangle = {{{(1/2)bh}}}, or {{{(1/2)(S + 3)(S + 2)}}}, or {{{((S + 3)(S + 2))/2}}}, or {{{(S^2 + 5S + 6)/2}}}
We then get: {{{S^2 = (S^2 + 5S + 6)/2}}}
{{{2S^2 = S^2 + 5S + 6}}} -------- Cross-multiplying
{{{2S^2 - S^2 - 5S - 6 = 0}}}
{{{S^2 - 5S - 6 = 0}}}
(S - 6)(S + 1) = 0  
S, or one side of square = {{{highlight_green(matrix(1,2,6, feet))}}} 
Length of triangle’s base: 6 + 3, or {{{highlight_green(matrix(1,2,9, feet))}}}
Height = 6 + 2, or {{{highlight_green(matrix(1,2, 8, feet))}}}