# The area of a rectangle is 192 square meter its diagonal is 20 in finds it width and length?

1
by kraken

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by kraken

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or 192 = LW

D = L^2 + W^2 equation

or 20 = L^2 + W^2

let W in terms in L in equation 2

and it comes up to this

W= sqroot(20 + L^2)

then

substitute the W from the equation 2 to equation 1

and the equation 1 becomes

192= L * sqroot(20 + L^2)

solving L using algebra skill

192/L = sqroot(20 + L^2)

square both sides to cancel the sqroot

36864 =L^2( 20 + L^2)

distribute L then

36864 = 20L^2 + L^4

then further simplification and algebra skills like an animal !!

you will get the value of L

L = 13.5 rounded off or 13.5 inches

then substitute L to equation 1

192= (13.5)W

then

W = 14.2222 or 14.2 inches!!

I hope it helps!!!