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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.
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Solution
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
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