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 sides of the rectangle each cutting together at right angles through the mid part of the field find (A) the area covered by road (B) the area of the field with out road (c) the cost to construct the road at the rate of rupees 50 square metre​

Answer 1

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.

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

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

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

Answer 2

Answer:

rupees 60000 is the question of answer