Question

A rhombus sheet whose perimeter is 40 m and one diagonal is 12 m long is painted on both sides at the rate of Rs.5 per m^2.The total cost of painting is ?

Answer 1

Let a rhombus ABCD where points are starting from top.

Perimeter=40m
Diagonal1=12m

Perimeter of rhombus=4×side
40=4×side
side=40/4
side=10m

DIAGONALS OF RHOMBUS BISECT EACH OTHER AT 90 degree.
So,If one diagonal is 12m then its half will be 6m.

TAKE ANY1 TRIANGLE MADE INSIDE RHOMBUS BY ITS DIAGONAL,
IN TRIANGLE ABO:(one angle is 90 degree)
by Pythagoras theoram:
${ab}^{2} = {bo}^{2} + {ao}^{2}$
IF BD(diagonal1) is 12 m then ao=6m (diagonals bisect each other at 90 degree)
ab=10m
ao=6m
${10}^{2} = {bo}^{2} + {6}^{2} \\ 100 = {bo}^{2} + 36 \\ {bo}^{2} = 100 - 36 \\ {bo}^{2} = 64 \\ bo = \sqrt{64} \\ bo = \sqrt{8 \times 8} \\ bo = 8m$
BO is half of diagonal BD
SO, BD=2×8=16m
we get diagonal2 which is 16m
diagonal1=12m (given)

AREA OF RHOMBUS= 1/2×diagonal1×diangonal2

=1/2×12×16
=6×16
=96 sq.m
area of rhombus at one side is 96 sq.m

total are of rhombus at front and at behind=2×96
=192 sq.m

COST OF PAINTING AT 1 SQ.M= Rs.5
Cost of painting at 192 sq.m= 192×5
= Rs.960

SO,
THE TOTAL COST OF PAINTING IS RS.960

HOPE IT HELPS YOU!

Answer 2

Answer: Total cost is Rs. 960

Step-by-step explanation:

Given, that the perimeter is 40m and the diagonal is 12m

$Perimeter=4\times side$

$\Rightarrow 40=4\times side$

$\therefore side=\frac{40}{4}=10 m$

We know, that in a rhombus, both diagonals bisect at $90\°$

So, if a diagonal is 12m long, its half will be 6m

In a triangle formed by two diagonals and a side

where the diagonals form $90\°$, we apply Pythagoras theorem to find the half of other diagonal

$6^2+(half\ of\ other\ diagonal)^2=10^2\\\Rightarrow (half\ of\ other\ diagonal)^2=100-36\\\Rightarrow (half\ of\ other\ diagonal)=\sqrt{64}\\\Rightarrow (half\ of\ other\ diagonal)=8$

$\therefore other\ diagonal\ is\ 8\times 2=16m long\\Area=\frac{1}{2}\times (product\ of\ lengths\ of\ the\ diagonals)\\=\frac{1}{2}\times 16\times 12\\=96m^2$

Given, that the cost to paint both sides is at the rate of $Rs. 5\ per\ m^2$

So, the total cost is $5\times 2\times 96=Rs.\ 960$

To know more about rhombus, click on the links below:

https://brainly.in/question/2486460

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