Question 499034
In this case since we know the ratio, we will modify the pathogorean formula to account for the ratio.

{{{(4*x)^2}}} + {{{(3*x)^2}}} = 37^2
{{{(4*x)^2}}} + {{{(3*x)^2}}} = 1369
16 * {{{x^2}}} + 9 * {{{x^2}}} = 1369
25{{{x^2}}} = 1369
{{{x^2}}} = 54.76
x = 7.4
7.4 * 3 = 22.2
7.4 * 4 = 29.6
{{{22.2^2}}} + {{{29.6^2}}} = 1369
492.84 + 876.16 = 1369
This does check.
The area will be 22.2 inches* 29.6 inches = 657.12 inches.
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{{{(9*x)^2}}} + {{{(16*x)^2}}} = 37^2
{{{(9*x)^2}}} + {{{(16*x)^2}}} = 1369
81 * {{{x^2}}} + 256 * {{{x^2}}} = 1369
337{{{x^2}}} = 1369
{{{x^2}}} = 4.06
x = 2.0
2 * 9 = 18
2 * 16 = 32
{{{18^2}}} + {{{32^2}}} = 1369
324+ 1024= 1368 (round off error)
This does check.
The area will be 18 inches * 32 inches = 576 inches
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Cleomenius