please answer this question breifly
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I think it will be correct one...
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The triangles are similar.
So ratio of their sides will be equal.
How the triangles are similar?
Well since DE is parallel to BC
corresponding angles will be equal
Angle ADE (D) = angle ABC(B)
and Angle AED(E) = angle ACB(C)
and angle BAC is common (A)
now if all three angles are equal there are similar
then
(AD/AB) = (AE/AC)
(4x-1)/(3x-1) = (8x-5)/(5x-3)
(4x-1)*(5x-3 + 4x-1)=(8x-5)*(3x-1+8x-5)
solving this gives x=1 or x= 1/2
So ratio of their sides will be equal.
How the triangles are similar?
Well since DE is parallel to BC
corresponding angles will be equal
Angle ADE (D) = angle ABC(B)
and Angle AED(E) = angle ACB(C)
and angle BAC is common (A)
now if all three angles are equal there are similar
then
(AD/AB) = (AE/AC)
(4x-1)/(3x-1) = (8x-5)/(5x-3)
(4x-1)*(5x-3 + 4x-1)=(8x-5)*(3x-1+8x-5)
solving this gives x=1 or x= 1/2
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