Answer:
The value of x is 5 units.
C is correct.
Step-by-step explanation:
We need to solve for x from the given figure.
In ΔADB and ΔCDB
∠ABD=∠BCD (Corresponding angle of two right triangle)
∠ADB=∠CDB (Each 90°)
∴ ΔADB ≈ ΔCDB By AA similarity
If two triangles are similar then ratio of their corresponding height are same.
[tex]\dfrac{BD}{DC}=\dfrac{AD}{BD}[/tex]
Substitute the value of side into the expression
[tex]\dfrac{10}{4x}=\dfrac{x}{10}[/tex]
Cross multiply and solve for x
[tex] 10\times 10=x\times 4x [/tex]
[tex]4x^2=100[/tex]
[tex]x^2=25[/tex]
[tex]x=\pm 5[/tex]
x can't be negative because side of triangle is positive.
Hence, The value of x is 5 units.
