Question

Help asap!!! Midterms

Answer 1

Answer:

The value of x is 5.

Step-by-step explanation:

Label the diagram such as

Given:

AD= x

DB= x +5

AE = x - 2

EC = x + 1

DE || BC

To Find:

x = ?

Solution:

Basic Proportionality Theorem:

"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".

DE || BC

∴ $\dfrac{AD}{DB}= \dfrac{AE}{EC}$ ...Basic Proportionality Theorem

Substituting the values in it we get

$\dfrac{x}{x+5}= \dfrac{x-2}{x+1}\\x(x+1)=(x+5)(x-2)\\\\x^{2}+x= x^{2}+3x-10\\ -2x=-10\\\\x=\dfrac{10}{2}=5\\ \\\therefore x =5$

The value of x is 5.