Question

in the figure for what value of x will be parallel to a b a d is equal to X + 10 d b is equal to 4 x + 10 Y is equal to X + 6 is equal to X + 10​

Answer 1

✤ We know -

Basic Proportionality Theorem states that "If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio".

✤ Solution -

In the given triangle ABC, DE ║ BC

$\sf{\dfrac{AD}{DB}=\dfrac{AE}{EC} }$

$\displaystyle{\sf{\longrightarrow \frac{x+10}{4x+10}=\frac{x+6}{x+10} }}\\\\\displaystyle{\sf{\longrightarrow (x+10)(x+10)=(x+6)(4x+10)}}\\\\\displaystyle{\sf{\longrightarrow (x+10)^2=4x^2+10x+24x+60}}\\\\\displaystyle{\sf{\longrightarrow x^2+100+20x=4x^2+34x+60}}\\\\\displaystyle{\sf{\longrightarrow 40=3x^2+14x}}\\\\\displaystyle{\sf{\longrightarrow 3x^2+14x-40=0}}\\\\\displaystyle{\sf{\longrightarrow 3x^2-6x+20x-40=0}}\\\\\displaystyle{\sf{\longrightarrow 3x(x-2)+20(x-2)=0}}$

$\displaystyle{\sf{\longrightarrow (x-2)(3x+20)=0}}\\\\\displaystyle{\sf{\longrightarrow x=2,\:\:x=\frac{-20}{3} }}$

❆ Length of a side can never be negative. So,

x = 2

$\underline{\rule{170}4}$

In the question, it has mentioned, "seg DE be parallel to AB".

$\leadsto$ It must be BC instead of AB.