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
We will be using the binomial probability formula to solve the problem
The formula is given by ⁿCₓ (p)ˣ (1-p)ⁿ⁻ˣ
Where:
n = the number of trials = 100
x = the number of samples we are trying on = 3
p = the probability of success = 2% = 0.02
We can either calculate ⁿCₓ by using the scientific calculator using the
button or by doing it manually use 
P(3) = ¹⁰⁰C₃ (0.02)³ (1 - 0.02)¹⁰⁰⁻³
P(3) = ¹⁰⁰C₃ (0.02)³ (0.98)⁹⁸
P(3) = 0.182 (rounded to three decimal places)
Correct answer: option 3
The formula is given by ⁿCₓ (p)ˣ (1-p)ⁿ⁻ˣ
Where:
n = the number of trials = 100
x = the number of samples we are trying on = 3
p = the probability of success = 2% = 0.02
We can either calculate ⁿCₓ by using the scientific calculator using the
P(3) = ¹⁰⁰C₃ (0.02)³ (1 - 0.02)¹⁰⁰⁻³
P(3) = ¹⁰⁰C₃ (0.02)³ (0.98)⁹⁸
P(3) = 0.182 (rounded to three decimal places)
Correct answer: option 3