For a plank in the shape of a parallelogram,t | vedclass

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Question

(C) parallelogram is divided into two congruent triangles by its diagonal. Let the sides of the triangle be $a = 12 \, cm$,$b = 17 \, cm$,and $c = 25

Vedclass · Accepted Answer

$540$

Vedclass · Answer

(C) parallelogram is divided into two congruent triangles by its diagonal. Let the sides of the triangle be $a = 12 \, cm$,$b = 17 \, cm$,and $c = 25 \, cm$.The semi-perimeter $s$ is calculated as $s = \frac{a + b + c}{2} = \frac{12 + 17 + 25}{2} = \frac{54}{2} = 27 \, cm$.Using Heron's formula,the area of one triangle is $\sqrt{s(s-a)(s-b)(s-c)} = \sqrt{27(27-12)(27-17)(27-25)} = \sqrt{27 	imes 15 	imes 10 	imes 2} = \sqrt{8100} = 90 \, cm^2$.The total area of the parallelogram is $2 	imes 90 = 180 \, cm^2$.The cost of painting at the rate of Rs. $3$ per $cm^2$ is $180 	imes 3 = 	ext{Rs. } 540$.

For a plank in the shape of a parallelogram,the adjacent sides measure $12 \, cm$ and $17 \, cm$,and one of its diagonals measures $25 \, cm$. Find the cost of painting the plank at the rate of Rs. $3$ per $cm^2$.

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