Question 197040
Find the length of the diagonal of a square patio with an area of 40 square meters.
.
Two steps...
First, find the length of one side of the square.
Let x = length of side of square
then
{{{x^2 = 40}}}
{{{x = sqrt(40)}}}
{{{x = sqrt(2*2*2*5)}}}
{{{x = 2sqrt(10)}}}
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Second, find diagonal using Pythagorean theorem:
Let d = diagonal
then
{{{(2sqrt(10))^2 + (2sqrt(10))^2 = d^2}}}
{{{(4(10)) + (4(10)) = d^2}}}
{{{40 + 40 = d^2}}}
{{{80 = d^2}}}
{{{sqrt(80) = d}}}
{{{sqrt(4*4*5) = d}}}
{{{4sqrt(5) = d}}}