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.

$\frac{CD}{AB} =\frac{DX}{BX} =\frac{CX}{AX}$

Now, using,

$\frac{CD}{AB} =\frac{DX}{BX}$

$\frac{CD}{AB=12} =\frac{DX=2.5}{BX=5}$

$\frac{CD}{12} =\frac{2.5}{5}$

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

$\frac{12*CD}{12} =\frac{12*2.5}{5}$

$\frac{1*CD}{1} =\frac{30}{5}$

$CD =\frac{6}{1}$

CD=6 Answer