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?

As shown in figure 1.57, 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?

Figure: Smaller pole PR = 4 m with shadow QR = 6 m; bigger pole AC = 8 m with shadow BC = x m; \(\angle R = \angle C = 90^\circ\).

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

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Answer: The shadow of the bigger pole is 12 m long.

At the same time the sun's rays make the same angle with the ground, so \(\angle PQR \cong \angle ABC\). Also \(\angle PRQ \cong \angle ACB = 90^\circ\).

So \(\triangle PRQ \sim \triangle ACB\) (AA test), and corresponding sides are in proportion:

\[\frac{PR}{AC} = \frac{QR}{BC}\] \[\frac{4}{8} = \frac{6}{x}\] \[x = \frac{6 \times 8}{4} = 12\]

Length of the shadow of the bigger pole = 12 m.

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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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?

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