The highest power of 12 that divides 273 (with remainder) is 
, and dividing gives
Divide the remainder term by the next highest power of 12,
.
So
, since
Divide the remainder term by the next highest power of 12,
So
The point of intersection of the diagonals of a rectangle is 4 cm further away from the smaller side than from the larger side o
f the rectangle. The perimeter of the rectangle is equal to 56 cm. Find the lengths of the sides of the rectangle.
1 answer:
We have that
If you draw a diagram, and draw perpendiculars from the intersection to the sides of the rectangle, you will see they are the mid point of each side.
see the attached figure
<span>If the mid point of the smaller side is ---------> x.
The mid point of the larger side will be -----------> (x + 4) </span>
The full length if the smaller side will be 2x and the length of the larger side will be 2(x + 4) = 2x + 8
The perimeter = 2 times the length + 2 times the width.
2(2x + 8) + 4x = 56
4x + 16 + 4x = 56
8x = 40
x = 5
Therefore
length = 2x + 8 = 18cm
<span>width = 2x = 10cm
</span>
the answer is
<span>the lengths of the sides of the rectangle are
</span>length = 18cm
width = 10cm
If you draw a diagram, and draw perpendiculars from the intersection to the sides of the rectangle, you will see they are the mid point of each side.
see the attached figure
<span>If the mid point of the smaller side is ---------> x.
The mid point of the larger side will be -----------> (x + 4) </span>
The full length if the smaller side will be 2x and the length of the larger side will be 2(x + 4) = 2x + 8
The perimeter = 2 times the length + 2 times the width.
2(2x + 8) + 4x = 56
4x + 16 + 4x = 56
8x = 40
x = 5
Therefore
length = 2x + 8 = 18cm
<span>width = 2x = 10cm
</span>
the answer is
<span>the lengths of the sides of the rectangle are
</span>length = 18cm
width = 10cm
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Answer:
A. length = 23 cm; width = 5 cm
Step-by-step explanation:
So if 4 times the width would be and 3 more than would be
, the equation would be
. If the perimeter is 56, then the new equation,
can be formed. This simplifies to
, then to
, then to
, and finally,
. So the width is 5, and now plug it into the first equation.
, becomes
, becomes
.
So the dimensions are: length = 23 cm, width = 5 cm.
*And just to be sure, which is correct.
Answer:
See Explanation
Step-by-step explanation:
The question has missing details. So, I'll solve using a general assumption.
Let one of the coordinates of the figure be
Let the scale factor be n
When dilated, the new figure is:
To return the image back to the original figure, the new scale factor mus be a reciprocal of the previous scale factor i.e.
So:
Substitute n(x,y) for A';
Take for instance:
-- scale factor
To get A from A', using the analysis above