Question

a rectangular field of 80 m long and 50 m broad has two roads each 10 m constructed are parallel to the side of the rectangle each cutting together at right angles through the mid part of the field find​

Answer 1

Answer:

1560rs

Step-by-step explanation:

The cost of gravelling them at Rs. 1.20 per square meter = Rs . 1560

To find the area of roads :

It is given that

a rectangular lawn 80 m × 60 m has two roads each 10 m wide running in the middle of it.

Dimension of two roads are 80×10 and 60×10

Area of two roads = 80×10+60×10−10×10

=800+600−100

= 1300 sq. meter

To find the cost for gravelling

It is given that

The cost of gravelling the at Rs. 1.20 per sq. meter.

Therefore total cost = total area × cost per sq. meter

=1300×1.20

=Rs.1560

∴ The cost of gravelling them at Rs. 1.20 per sq. meter = Rs. 1560

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Answer 2

Step-by-step explanation:

GIVEN :-

• Length of Rectangle = 80 m.

• Breadth of Rectangle = 50 m.

• Width of road = 10 m.

TO FIND :-

• the area covered by road .

• the area of the field with out road .

• the cost to construct the road at rate of Rs. 50 /m².

SOLUTION :-

As we know that the area of rectangle is given by,

$\\ : \implies \displaystyle \sf \: Area_{(field)} = length \times breadth$

$: \implies \displaystyle \sf \: Area_{(field)} = 80 \: m \times 50 \: m$

$: \implies \underline{ \boxed{\displaystyle \sf \: \bold{ Area_{(field)} = 4000 \: m ^{2} }}}$

Now we are finding the area of the road which is parallel to the length of the rectangular field,

$\\ : \implies \displaystyle \sf \: Area_{(road)} = length \: \times width$

$: \implies \displaystyle \sf \: Area_{(road)} = 80 \: m \times 10 \: m$

$: \implies \underline{ \boxed{\displaystyle \sf \: \bold{ Area_{(road)} = 800 \: m ^{2} }}}$

Now we are finding the area of the road which is parallel to the breadth of the rectangular field,

$\\ : \implies \displaystyle \sf \: Area_{(road)} = breadth \times width$

$: \implies \displaystyle \sf \: Area_{(road)} = 50 \: m \times 10 \: m$

$: \implies \underline { \boxed{\displaystyle \sf \: \bold{ Area_{(road)} = 500 \: m ^{2} }}}$

Now , If two roads are intersecting each other at a point . So that point is repeated two times i.e one road is coming which is parallel to the length and the other one which is parallel to the breadth . So , we will find the area of common portion now,

$\\ : \implies \displaystyle \sf \: Area_{(common)} = width \times width$

$: \implies \displaystyle \sf \: Area_{(common)} = 10 \: m \times 10 \: m$

$: \implies \underline{ \boxed{ \displaystyle \sf \: \bold{ Area_{(common)} = 100 \: m ^{2} }}}$

Now we are finding the area covered by the roads which is equal to the area covered by Both the roads,

$\\ : \implies \displaystyle \sf \: Area_{(both \: road)} = 800 + 500 - (area_{(common)})$

$: \implies \displaystyle \sf \: Area_{(both \: road)} =1300 - 100 \: m ^{2}$

$: \implies \underline { \boxed{ \displaystyle \sf \: \bold{ Area_{(both \: road)} =1200 \: m ^{2} }}}$

Now we are finding the cost to construct the road at rate of Rs. 50 /m².

$\\ : \implies \displaystyle \sf \: cost_{(construction)} = area \times rate$

$: \implies \displaystyle \sf \: cost_{(construction)} = 1200 \times 50$

$: \implies \underline{ \boxed{ \displaystyle \sf \: \bold{ cost_{(construction)} = \: rs. \: 60000 \: }}}$