Abcd is a quadrilateral with ba parallel to cd. ac and bd meet at x where x =8cm and xa=10cm.if bd=27,then find the length of bx
Answers
The length of BX is 15 cm.
Step-by-step explanation:
Referring to the figure attached below, we have
ABCD is a quadrilateral with BA // CD
AC and BD intersect at X
CX = 8 cm
XA = 10 cm
BD = 27 cm
Let's consider ΔBXA and ΔDXC, we have
∠BXA = ∠DXC ...... [∵BA // CD, vertically opposite angles]
∠ABX = ∠CDX ...... [∵ BA // CD, alternate angles]
∴ By AA similarity, ΔBXA ~ ΔDXC
We know that the corresponding sides of similar triangles are proportional to each other.
∴ BX/DX = XA/CX
⇒ BX/(BD - BX) = XA/CX
substituting the values of BD, AX & CX
⇒ BX/(27-BX) = 10/8
⇒ 8BX = 10 (27 - BX)
⇒ 8BX = 270 - 10BX
⇒ 18BX = 270
⇒ BX = 15 cm
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