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

Sagot :

Kaizoku00idn
A = L x W  equation 1                                      let D = diagonal
or 192 = LW

D = L^2 + W^2    equation 2
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!!!