A rhombus-shaped sheet with a perimeter of 40 | vedclass

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(D) $1$. The perimeter of the rhombus is $40 \, cm$. Since all sides of a rhombus are equal,the side length $a = 40 / 4 = 10 \, cm$.$2$. Let the diago

Vedclass · Accepted Answer

$960$

Vedclass · Answer

(D) $1$. The perimeter of the rhombus is $40 \, cm$. Since all sides of a rhombus are equal,the side length $a = 40 / 4 = 10 \, cm$.$2$. Let the diagonals be $d_1 = 12 \, cm$ and $d_2$. In a rhombus,diagonals bisect each other at right angles. Using the Pythagorean theorem on one of the four right-angled triangles formed by the diagonals,we have $(d_2 / 2)^2 + (d_1 / 2)^2 = a^2$.$3$. $(d_2 / 2)^2 + (12 / 2)^2 = 10^2 \implies (d_2 / 2)^2 + 36 = 100 \implies (d_2 / 2)^2 = 64 \implies d_2 / 2 = 8 \implies d_2 = 16 \, cm$.$4$. The area of the rhombus is $(d_1 	imes d_2) / 2 = (12 	imes 16) / 2 = 96 \, cm^2$.$5$. Since the sheet is printed on both sides,the total area to be printed is $96 	imes 2 = 192 \, cm^2$.$6$. The cost of printing is $192 	imes 5 = Rs. \, 960$.

$A$ rhombus-shaped sheet with a perimeter of $40 \, cm$ and one diagonal of $12 \, cm$ is printed on both sides at the rate of $Rs. \, 5$ per $cm^2$. Find the total cost of printing.

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