Question 1078749

A triangle has a side length of 3 inches and an area of 22 square inches.  A similar triangle has a corresponding side length of 6 sinches.  Find the area of the larger triangle.
<pre>The ratio of the corresponding sides of 2 similar TRIANGLES is equal to the square root of the ratio of their areas.
Ratio of one of smaller triangle's sides to corresponding side of larger triangle: {{{3/6}}}
Let the area of the larger triangle be A
With the area of the smaller triangle being 22 sq inches, we get: {{{3/6 = sqrt(22)/sqrt(A)}}}
{{{1/2 = sqrt(22)/sqrt(A)}}} ------- Reducing {{{3/6}}}
{{{1^2/2^2 = (sqrt(22)^2)/(sqrt(A)^2)}}} ------- Squaring both sides 
{{{1/4 = 22/A}}}
Cross-multiplying, we get the area of larger triangle, or: {{{highlight_green(matrix(1,7, A, "=", 4(22), "=", 88, square, inches))}}}