Question

Help asap!!! Midterms

Answer 1

The value of x is 5.

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

∴
`(AD)/(DB)= (AE)/(EC)` ...Basic Proportionality Theorem

Substituting the values in it we get

`(x)/(x+5)= (x-2)/(x+1)\\x(x+1)=(x+5)(x-2)\\\\x^(2)+x= x^(2)+3x-10\\  -2x=-10\\\\x=(10)/(2)=5\\ \\\therefore x =5`

The value of x is 5.