Question

7 pillars are used to hold a slant rod as shown in the figure. If the distance between every two pillars is 1 m and first pillar is 1 m from the rod leg. Height of the last pillar is 10.5 m. Find the height of first pillar.

• A. 1.5
• B. 2.5
• C. 3.5
• D. 0.5

Answer 1

The correct option is A 1.5

Let
PQ be the first pillar, AB be the last pillar and AC be the slant rod. x is the height of the first pillar to be found.

From the given figure, AP and QB are transversals for parallel lines PQ and AB.
$\angle P=\angle A$ [Corresponding angles are equal]
$\angle Q=\angle B$ [Corresponding angles are equal]
and $\angle C$ is common angle for both triangles.

Since, three corresponding angles for two triangles are equal. $\Delta ABC\text{and}\Delta PQC$ are similar, so their sides will be proportional.
$\Rightarrow \frac{PQ}{AB}=\frac{CQ}{CB}\Rightarrow \frac{x}{10.5}=\frac{1}{1+6}\Rightarrow x=\frac{10.5}{7}x=1.5m$