Julian wants her rectangular garden to cover an AREA of 180 square feet what bare the LENGTHS AND WIDTHS of two possible rectang
1 answer:
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A regular trapezoid is shown in the picture attached.
We know that:
DC = minor base = 4
AB = major base = 7
AD = BC = lateral sides or legs = 5
Since the two legs have the same length, the trapezoid is isosceles and we can calculate AH by the formula:
AH = (AB - DC) ÷ 2
= (7 - 5) ÷ 2
= 2 ÷ 2
= 1
Now, we can apply the Pythagorean theorem in order to calculate DH:
DH = √(AD² - AH²)
= √(5² - 1²)
= √(25 - 1)
= √24
= 2√6
Last, we have all the information needed in order to calculate the area by the formula:
A = (7 + 5) × 2√6 ÷ 2
= 12√6
The area of the regular trapezoid is 12√6 square units.
We know that:
DC = minor base = 4
AB = major base = 7
AD = BC = lateral sides or legs = 5
Since the two legs have the same length, the trapezoid is isosceles and we can calculate AH by the formula:
AH = (AB - DC) ÷ 2
= (7 - 5) ÷ 2
= 2 ÷ 2
= 1
Now, we can apply the Pythagorean theorem in order to calculate DH:
DH = √(AD² - AH²)
= √(5² - 1²)
= √(25 - 1)
= √24
= 2√6
Last, we have all the information needed in order to calculate the area by the formula:
A = (7 + 5) × 2√6 ÷ 2
= 12√6
The area of the regular trapezoid is 12√6 square units.
Answer:
Equations with one solution:
Equations with no solution:
Equations with infinite many solutions:
Step-by-step explanation:
We will solve each equation to see if it has one solution, no solution or infinite many solutions.
An equation where the value of variable can be found has one solution.
An equation with no solution has both sides different.
An equation with infinite solution will have both sides equal after solution(number)
So,
<u>Equation 1:</u>
5(x-2) = 5x-7
As both sides are not equal, equation has no solution.
<u>Equation 2:</u>
As both sides are equal the equation has infinite many solutions.
<u>Equation 3:</u>
As x=3, the equation has only one solution.
<u>Equation 4:</u>
The equation has no solution.
Hence,
Equations with one solution:
Equations with no solution:
Equations with infinite many solutions: