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
You might be interested in
You just need to equate the expressions to find the values for a,b and c. First, let's settle that 2^5/4=8, and 8 is 2^3. Also, an important tool here is the indicie rule:
1st expression: 2^5/4=8
2nd expression: It tells us that 2^5/2^a=2^3 (I know that this equals to 8 as all the expressions are equal therefore is the same as our first expression). Using the indicie law, this means that a=2
3rd expression: 2^b must equal to 8 as well, so b=3
4th expression: c=8 as all of the other expressions we have figured out equal to 8
So a=2, b=3 and c=8
1st expression: 2^5/4=8
2nd expression: It tells us that 2^5/2^a=2^3 (I know that this equals to 8 as all the expressions are equal therefore is the same as our first expression). Using the indicie law, this means that a=2
3rd expression: 2^b must equal to 8 as well, so b=3
4th expression: c=8 as all of the other expressions we have figured out equal to 8
So a=2, b=3 and c=8