Let's look at the picture, let's imagine that the gray line is the perimeter fence and that the red OR the blue is the one dividing it. We can see that the blue line is longer than the red one, so it will be advantageous, to have a bigger area, to have the dividing fence the smallest possible.
Let's say then that the width (W) is bigger (or equal) to the length (L), so we have:
The area is W*L, so we have
this function is a parabola facing down, its zeros are 0 and 80, therefore its maximum is when L=40
hence, L=40 and W=(240-120)/2=60
It will be a rectangle, measuring 60x40 and the divinding fence will be 40
All sides of a triangle add up to 180 degrees. Since we know one angle is 93 degrees, we know that the top part is going to equal 180 degrees. We know that two of those measurements are 93 and 45, so we add those together to get 138. We subtract this from 180 to find the missing angle, which is 42 degrees. So, the left side of the triangle is equivalent to 45 degrees and the right side (x) is 42 degrees. 93 + 45 + 42 = 180. If it was asking for the measurements of the supplementary angles to the bottom angles of the triangle, then those would be (for 45) 135 and (for 42) 138, that way both angles and their supplements add up to 180 each. I hope this helps and that it’s right
<u>Corrected Question</u>
Quadrilateral QRST is inscribed in circle W as shown below. The measure of ∠QRS is 12 degrees less than three times the measure of ∠QTS and
mRQT=mRST .
(a)Determine the measure of Angle QTS .
(b)What is the common measure of angles RQT and RST ?
Answer:
(a)48 degrees
(b)90 degrees
Step-by-step explanation:
Theorem: Opposite angles of a cyclic quadrilateral are supplementary.
(a)
Let the measure of ∠QTS=x
Therefore: m∠QRS=3x-12
∠QTS and ∠QRS are opposite angles of a cyclic quadrilateral. By the theorem above:
x+3x-12=180
4x=180+12
4x=192
x=48 degrees
The measure of angle QTS is 48 degrees.
(b)Since mRQT=mRST
mRQT and mRST are opposite angles of a cyclic quadrilateral
Therefore:
mRQT+mRST=180 degrees
2mRQT=180
mRQT=90 degrees
Therefore, the common measure of RQT and RST is 90 degrees.
Answer:
x = 77.8 square yards
Step-by-step explanation:
Given the following data;
Area = 700 square feet
To find the area in square yards;
Conversion:
1 yard = 3 feet
1 square yard = 9 square feet
x square yard = 700 square feet
Cross-multiplying, we have;
700 = 9x
x = 700/9
x = 77.8 square yards
Answer: x=2
√
10
, -2
√
10
