Question

An advertisement board is in the form of an isosceles triangle with perimeter 36 m and each of the equal sides are 13 m. Find the cost of painting it at ₹ 17.50 per square metre.

Answer 1

Equal sides of a triangle = 13 m

Perimeter of an isosceles triangle = 36 m

Length of the third side = 36 – (13 + 13) m

= 36 – 26

= 10 m

Here a = 13 m, b = 13 m and c = 10 m

s = `("a" + "b" + "c")/2`

= `(13 + 13 + 10)/2`

= `36/2`

= 18 m

s – a = 18 – 13 = 5 m

s – b = 18 – 13 = 5 m

s – c = 18 – 10 = 8 m

= `sqrt("s"("s" - "a")("s" - "b")("s" - "c"))`

= `sqrt(18 xx 5 xx 5 xx 8)`

= `sqrt(2 xx 3^2 xx 5^2 xx 2^3)`

= `sqrt(2^4 xx 3^2 xx 5^2)`

= 2² × 3 × 5

= 60 sq.m

Cost of painting for one sq. m = ₹ 17.50

Cost of painting for 60 sq. m = ₹ 60 × 17.50

= ₹ 1050