3 times the sum of a number and 3
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Given:
Consider the below figure attached with this equation.
Quadrilateral QRST is a parallelogram.
To find:
The value of x.
Solution:
We know that the sum of two consecutive interior angles of a parallelogram is 180 degrees because they are supplementary angles.
In parallelogram QRST,
On comparing both sides, we get
Divide both sides by 12.
Therefore, the value of x is 16.
Answer: The expressions for the length and width of the new patio are
And the area of the new patio is 384 sq. feet.
Step-by-step explanation: Given that Stephen has a square brick patio. He wants to reduce the width by 4 feet and increase the length by 4 feet.
The length of one side of the square patio is represented by x.
We are to write the expressions for the length and width of the new patio and then to find the area of the new patio if the original patio measures 20 feet by 20 feet.
Since Stephen wants to reduce width of the patio by 4 feet, so the width of the new patio will be
The length of the patio is increased by 4 feet, so the length of the new patio will be
Now, if the original patio measures 20 feet by 20 feet, then we must have
and
Therefore, the area of the new patio is given by
Thus, the expressions for the length and width of the new patio are
And the area of the new patio is 384 sq. feet.
now, let's recall Cavalieri's Principle, "solids with equal altitudes and cross-sectional areas at each height, have the same volume".
so, even though this cylinder is slanted, it has the same cross-sectional area as a cylinder that's straight-up, whose altitude is h = 5, and radius r = 4.