Observe the rectangle below.
x>0
If the area of the rectangle is:
.
Calculate x.
Observe the rectangle below.
\( x>0 \)
If the area of the rectangle is:
\( x^2-13 \).
Calculate x.
The rectangle ABCD is shown below.
AB = X
The ratio between AB and BC is \( \sqrt{\frac{x}{2}} \).
The length of diagonal AC is labelled m.
Determine the value of m:
Given the rectangle ABCD
AB=X the ratio between AB and BC is equal to\( \sqrt{\frac{x}{2}} \)
We mark the length of the diagonal \( A \) with \( m \)
Check the correct argument:
Given the rectangle ABCD
AB=Y AD=X
The triangular area DEC equals S:
Express the square of the difference of the sides of the rectangle
using X, Y and S:
Shown below is the rectangle ABCD.
AB = y
AD = x
Express the square of the sum of the sides of the rectangle using the area of the triangle DEC.
Observe the rectangle below.
x>0
If the area of the rectangle is:
.
Calculate x.
First, recall the formula for calculating the area of a rectangle:
The area of a rectangle (which has two pairs of equal opposite sides and all angles are ) with sides of length units, is given by the formula:
(square units)
After recalling the formula for the area of a rectangle, let's proceed to solve the problem:
Begin by denoting the area of the given rectangle as: and proceed to write (in mathematical notation) the given information:
Continue to calculate the area of the rectangle given in the problem:
Using the rectangle area formula mentioned earlier:
Continue to simplify the expression that we obtained for the rectangle's area, using the distributive property:
We are able to obtain the area of the rectangle by
using the distributive property as shown below:
Recall the given information:
Therefore, we can conclude that:
We solved the resulting equation simply by combining like terms, isolating the expression with the unknown on one side and dividing both sides by the unknown's coefficient in the final step,
Note that this result satisfies the domain of definition for x, which was given as:
-1\text{<}x\text{<}4 and therefore it is the correct result
The correct answer is answer C.
The rectangle ABCD is shown below.
AB = X
The ratio between AB and BC is .
The length of diagonal AC is labelled m.
Determine the value of m:
We know that:
We also know that AB equals X.
First, we will substitute the given data into the formula accordingly:
Now let's look at triangle ABC and use the Pythagorean theorem:
We substitute in our known values:
Finally, we will add 1 to both sides:
Given the rectangle ABCD
AB=X the ratio between AB and BC is equal to
We mark the length of the diagonal with
Check the correct argument:
Let's find side BC
Based on what we're given:
Let's divide by square root x:
Let's reduce the numerator and denominator by square root x:
We'll use the Pythagorean theorem to calculate the area of triangle ABC:
Let's substitute what we're given:
Given the rectangle ABCD
AB=Y AD=X
The triangular area DEC equals S:
Express the square of the difference of the sides of the rectangle
using X, Y and S:
Since we are given the length and width, we will substitute them according to the formula:
The height is equal to side AD, meaning both are equal to X
Let's calculate the area of triangle DEC:
Let's substitute the given data into the formula above:
Shown below is the rectangle ABCD.
AB = y
AD = x
Express the square of the sum of the sides of the rectangle using the area of the triangle DEC.