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anyanavicka [17]
2 years ago
8

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.

Mathematics
1 answer:
Nady [450]2 years ago
7 0
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

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