Question

A plot of ground in the form of an isosceles triangle is turfed for ₹ 15 at 25 paise per sq. meter. Find the length of each of the equal sides if its base is 24 metres.

Answer 1

Given: A plot in the shape of an isosceles triangle is turfed for ₹ 15 at 25 paise per sq. metre; the base = 24 m.

Step-wise calculation:

1. Convert rate:

25 paise

= ₹ 0.25 per m²

2. Area = `"Cost"/"Rate"`

= 15 ÷ 0.25

= 60 m²

3. For a triangle,

Area = `1/2` × base × height 

So, 60 = `1/2 xx 24 xx h`

⇒ 60 = 12h

⇒ h = 5 m

4. Half the base

= `24/2`

= 12 m

Each equal side (by Pythagoras)

= `sqrt(("half base")^2 + "height"^2)` 

= `sqrt(12^2 + 5^2)`

= `sqrt(144 + 25)`

= `sqrt(169)`

= 13 m

Each of the equal sides is 13 metres.