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3 years ago

What is true about the dilation?

Mathematics

1 answer:

Lana71 [14]3 years ago

7 0

Answer:

- It is a reduction with a scale factor between 0 and 1.

- It is an enlargement with a scale factor greater than 1.

Step-by-step explanation:

1. Dilation is defined as a transformation of an image in which the size on this image changes but its shape does not change.

2. In dilation, to obtain the new dimensions of the image you must multiply the dimensions of the original image by a number called "Scale factor".

3. When the scale factor is greater than 1 it is an enlargement and when this is between 0 and 1, it is a reduction.

tysm for the answer, i did the work-

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The area of rectangular field is 1440 sq meters and perimeter is 152 metre. Out of length or breadth which one is to be decrease

Arturiano [62]

Answer:

If Length is decreased by 10% then it would become a square.

Step-by-step explanation:

Given:

Area of Rectangular field = 1440 sq. m

Perimeter = 152 m.

We need to find which one needs to be decreased by what percentage to make it a square.

Solution:

Let length be denoted by 'l'.

Also Let width be denoted by 'w'.

Now we know that Area of rectangular field is given by Length times width.

framing in equation form we get;

$l\times w = 1440 \ \ \ \ equation\ 1$

Also we know that Perimeter of rectangular field is given by 2 times sum of Length and width.

framing in equation form we get;

$2(l+w) =152\\\\l+w =\frac{152}{2}\\\\l+w=76\\\\l=76-w \ \ \ \ equation \ 2$

Now Substituting equation 2 in equation 1 we get;

$l\times w =1440\\\\(76-w)w=1440\\\\76w-w^2=1440\\\\w^2-76w+1440 =0$

Now we will find the root by factorizing the same we get;

$w^2-36w-40w+1440=0\\\\w(w-36)-40(w-36)=0\\\\(w-36)(w-40) =0 \\$

Now solving for each to find the value of 'w' we get;

$w-36 =0\\\\w=36\\\\also \\\\w-40=0\\\\w=40$

So We can say that;

Width = 36 m and Length = 40 m

Now we need to find out of length or breadth which one is to be decreased by what percentage to make it a square.

We know that square has all sides same.

So from the data we found we can say that if length is decreased by 4 then length and breadth(width) both will be equal.

So to find percentage decreased we will divide length to be decreased by total length and then multiply by 100.

framing in equation form we get;

percentage decreased = $\frac{4}{40}\times 100 = 10\%$

Hence If Length is decreased by 10% then it would become a square.

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