Question

Your Turn: In the diagram, AB = 12, DX = 2.5, and BX = 5. Find CD. Show all work.

Answer 1

answer is 6.5 as the two triangles are similar

Answer 2

Your Turn: In the diagram, AB = 12, DX = 2.5, and BX = 5. Find CD. Show all work.

Solution:

In ΔABX and ΔCDX,

∠CDX=∠ABX=90°

Also,∠CXD=∠AXB (as shown in figure)

∠DCX=∠BAX, as two angles of the triangle are equal. The third angle is also equal.

So ΔCDX≈ΔABX

Hence, the ratio of sides must be equal.

`(CD)/(AB) =(DX)/(BX) =(CX)/(AX)`

Now, using,

`(CD)/(AB) =(DX)/(BX)`

`(CD)/(AB=12) =(DX=2.5)/(BX=5)`

`(CD)/(12) =(2.5)/(5)`

Now, To solve for CD, Let us multiply by 12 on both sides

`(12*CD)/(12) =(12*2.5)/(5)`

`(1*CD)/(1) =(30)/(5)`

`CD =(6)/(1)`

CD=6 Answer