what will be the area of a rectangle if its length is halved and breadth is 4 times?
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Answers
Let l = the length of a rectangle.
Let w = the breadth or width of a rectangle.
The area A of a rectangle is given by the formula:
A = lw
Now, if the length l of a rectangle is doubled, then the new length is 2l. In addition, if the breadth or width w of a rectangle is reduced by half, then the new width is w - (1/2)w = (1)w - (1/2)w
= (2/2)w - (1/2)w
= [(2/2) - (1/2)]w
= [1/2]w
= w/2
To see how these changes in the length and in the width affect the area A of a rectangle, we substitute the new length and width into the area formula as follows:
A = 2l(w/2)
= (2/2)lw
= (1)lw
= lw
We now see that there is NO CHANGE in the area A of a rectangle if we double its length and also reduce its width by one-half.
Answer:
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Let l = the length of a rectangle.
Let w = the breadth or width of a rectangle.
The area A of a rectangle is given by the formula:
A = lw
Now, if the length l of a rectangle is doubled, then the new length is 2l. In addition, if the breadth or width w of a rectangle is reduced by half, then the new width is w - (1/2)w = (1)w - (1/2)w
= (2/2)w - (1/2)w
= [(2/2) - (1/2)]w
= [1/2]w
= w/2
To see how these changes in the length and in the width affect the area A of a rectangle, we substitute the new length and width into the area formula as follows:
A = 2l(w/2)
= (2/2)lw
= (1)lw
= lw
We now see that there is NO CHANGE in the area A of a rectangle if we double its length and also reduce its width by one-half.
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