Question

The width of a rectangle is 5 feet, and the diagonal is 8 feet. Which is the area of the rectangle? (Round to nearest hundredth.)

Answer 1

$The \ formula \ for \ the \ area \ of \ a \ rectangle \ is: \\\\A=l\cdot w\\ where \ l \ is \ the \ length, \ w \ is \ the \ width \\\\ w = 5 \feet , \\ diagonal: \ d= 8 \ feet \\ \\ apply \ the \ Pythagorean \ Theorem:$

$d^2=w^2+l^2 \\ \\l^2=d^2-w^2\\\\l^2=8^2-5^2\\\\l^2=64-25\\\\l^2=39$

$l=\sqrt{39}\\\\l \approx 6.244998 \ feet\\\\A= 6.244998 * 5= 31.22499\approx 31.23 \ feet^2$