Carmen is dividing her rectangular garden with a diagonal fence. The length of the garden is 11 feet and the diagonal is 19 feet. Which equation can be used to find the width of the garden? How wide is the garden? Select two answers.
A.11^2+w^2=19^2
B.19−11=w
C.width = 8 feet
D.width = 15.5 feet
A and D I did the math 11 squared is 121 and 19 squared is 361 so I subtracted 121 from 361 and got 240 and 15.5 times 15.5 equals 240 so it's 15.5 hope this helps
clearly A, from the Pythagorean Theorem.
Now just solve for w.
Clearly the first
A.11^2+w^2=19^2
Reason be is that with the diagonal crossing the rectangular garden
It immediately forms a right angle triangle
Which give rises to the Pythagoras theorem
11²+w²=19²
W²=19²-11²
W=√(19²-11²)
Well, this is a puzzling situation, isn't it? To find the width of Carmen's garden, we can make use of some mathematical wizardry.
Now, if we take a moment to think about it, we can see that the diagonal of the garden creates a right triangle with the width and length as the two legs. And if you recall your Pythagorean theorem, it states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
So, by encoding this information into an equation, we get A. 11^2 + w^2 = 19^2. This equation allows us to determine the width of Carmen's garden.
Now, let's do some calculations to solve this riddle. If we plug in the values, we get 121 + w^2 = 361. By subtracting 121 from both sides, we find w^2 = 240. Taking the square root of both sides, we get w = approximately 15.49, which we can round up to 15.5 feet.
So, the width of Carmen's garden is definitely 15.5 feet. And the equation that can be used to find it is A. 11^2 + w^2 = 19^2.
To find the width of the garden, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides.
In this case, the length of the garden is 11 feet, and the diagonal is 19 feet. We need to find the width, which can be represented by w.
Using the Pythagorean theorem, we can set up the equation: w^2 + 11^2 = 19^2
Therefore, the correct equation to find the width of the garden is A. 11^2 + w^2 = 19^2.
To find the width, we can now solve this equation using algebraic manipulations:
w^2 + 121 = 361 (since 11^2 = 121 and 19^2 = 361)
Subtracting 121 from both sides, we get:
w^2 = 240
Taking the square root of both sides, we find:
w = √240
The width of the garden is approximately 15.5 feet.
Therefore, the correct answers are:
A. 11^2 + w^2 = 19^2
D. width = 15.5 feet