Question

In the diagram, the length of segment BC is 23 units. What is the length of segment DC? 3 units 8 units 13 units 33 units

Answer 1

The length of segment DC is 33 unit.

Explanation:

As given

The length of segment BC is 23 units.

As given in the figure .

AB = 2x + 7

AB = BC

2x + 7 = 23

2x = 23 - 7

2x = 16

`x = (16)/(2)`

x = 8

In the Δ ABD and ΔCBD

(1) AB = BC

(As given in the figure.)

(2) ∠DBA = ∠DBC = 90°

(3) BD = BD

(Common side of both the triangle.)

Thus by using SAS congurence property .

Δ ABD ≅ ΔCBD

Thus

AD = DC

(Corresponding sides of the congurent triangle.)

Thus

AD = 4x + 1

Put x = 8

AD = 4 × 8 + 1

= 32 + 1

= 33 unit

Thus AD = DC = 13 unit

Therefore the length of segment DC is 33 unit.

Answer 2

based on the drawing both sides are the same length

so knowing BC = 23 you need to find the value of x and put it in the formula for the side

23=2x+7

16 = 2x

x=8

4x+1 = 4(8)+1 = 33 units