In the given figure, XZ is parallel to BC. AZ = 3 cm, ZC = 2 cm, BM = 3 cm and MC = 5 cm. Find the length of XY.

Question

Q) In the given figure, XZ is parallel to BC. AZ = 3 cm, ZC = 2 cm, BM = 3 cm and MC = 5 cm. Find the length of XY.

Sapling Academy · Accepted Answer

Step 1: Since XZ ǁ BC, Therefore, $\frac{AX}{AB} = \frac{AZ}{AC}$ (BPT Theorem)

∴ $\frac{AX}{AB} = \frac{AZ}{AZ + ZC} = \frac{3}{3 +2} = \frac{3}{5}$ .............. (i)

Step 2: Since XZ ǁ BC,   ∴  XY ǁ BM

∠ AXY  = ∠ ABM      (Corresponding angles)

∠ XAY  = ∠ BAM       (Common angle)

∴ Δ AXY $\sim$ Δ ABM    (by AA property)

∴   $\frac{AX}{AB} = \frac{XY}{BM}$

Step 3: Substituting value from equation (i), we get:

$\frac{3}{5} = \frac{XY}{3}$

or XY =  $\frac{9}{5}$ = 1.8

Therefore, the value of XY is 1.8 cm.

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