Question

hlo mates

A rhombus sheet whose perimeter is 32 m and whose one diagonal is 10 m long,is
painted on both sides at the rate of Rs 5 per m². Find the cost of painting.
$\mathfrak \red{p} \blue{l} \green{z} \: \pink{give} \: \purple{answer}$
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Answer 1

Refer to attachment..

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$\huge{\underline{\mathbb{\pink{Thankyou}}}}$

Answer 2

$\underline \mathbb{SOLUTION}$

$\bold\green{\underline{Given\:that}}$

》Perimeter of rhombus = 32 m.

$\bold\green{\underline{We\:know}}$

》Perimeter = 4a

$\bold\green{\underline{Then\:ATQ:-}}$

$= > 4a = 32$

$= > side = 8m$

$\boxed {SIDE(AB)= 8m}$

》Diagonal AC = 10m

And,

》OA = 1/2 AC

$= > \frac{1}{2} \times 10$

$= > side = 5m$

$\boxed {SIDE(OA)= 5m}$

$\bold\green{\underline{From\:Pythagoras:-}}$

$= > ob = {ab}^{2} - {oa}^{2}$

$= > ob = \sqrt{ {8}^{2} - {5}^{2} }$

$= > ob = \sqrt{64 - 25}$

$= > ob = \sqrt{39} m$

$\underline \mathbb{NOW,}$

》BD = 2 OB = 2√39 m

$= > area \: of \: sheet = \frac{1}{2} \times bd \times ac$

$= > \frac{1}{2} \times 2 \sqrt{39} \times 10 = 10 \sqrt{39} {m}^{2}$

》COST OF PAINTING at rate of 5 metre square

$= > \frac{1}{2} \times 2 \sqrt{39} \times 10$

$= > cost = rs.625$

$\boxed {COST= Rs.625}$

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