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Question
As shown in figure, two poles of height 8 m and 4 m are perpendicular to the ground. If the length of shadow of smaller pole due to sunlight is 6 m then how long will be the shadow of the bigger pole at the same time?
Solution
PR and AC are two poles. QR and BC are their shadows respectively.
PR = 4, RQ = 6, AC = 8 ...(Given)
The shadows are cast at the same time.
∴ ΔPQR ∼ ΔABC
∴ `"PR"/"AC" = "QR"/"BC"` ...(Corresponding sides of similar triangles are in proportion)
∴ `4/8 = 6/x`
∴ `x = (8 × 6)/4`
∴ x = 12
∴ BC = 12m
The length of the shadow of the bigger pole is 12 m.
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