In an isosceles triangle △ABC with base of AB=8, points K and L are marked on sides AC and BC accordingly, such that KL∥ AB. It turns out that △BLK and △AKB are also isosceles triangles. What can be the length of CL?

CL = (KL × CB)/8

Step-by-step explanation:

First we would draw the diagram obtained from the given information. Then find the relationship that enable us find length of CL.

Find attached the diagram

Given:

△ABC is an isosceles triangle

KL || AB

AB =8

△BLK and △AKB are also isosceles triangles

From our diagram,

AC = CB (two sides of an isosceles triangles are equal)

∆KCL is similar to ∆ACB

In similar triangles theorem, the ratio of their corresponding sides are equal

KC/AC = LC/BC

Quadrilateral KLAB is an isosceles trapezium:

KL is parallel to AB

∠A = ∠B (opposite base angles are equal)

KA = KL (opposite sides are equal)

The diagonals are congruent

AL ≅ KB

△BLK and △AKL are also isosceles triangles.

BL = AK

∠L = ∠K (opposite base angles are equal)

LK = KL

AL = KB

Also from similar triangles: KL/AB = KC/AC

KL/8 = KC/AC

KC/AC = KL/8

KC/AC = LC/BC

Therefore: KL/8 = LC/BC

Cross multiplying

8CL = KL × CB

CL = (KL × CB)/8

45

step-by-step explanation:

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b