Answer:
The rectangle's area is 48 square meters
Step-by-step explanation:
Recall that the perimeter of a rectangle of base b and height h is given by the formula:
Perimeter = 2 b + 2 h
we know that the perimeter is 28 meters, then we can create our first equation;
2 b + 2 h = 28
which means:
2 (b + h) = 28
b + h = 28/2
b + h = 14
the tell us that the diagonal is 10 meters, so we use the Pythagorean theorem to write a second equation using the rectangle's base, height, and diagonal (which form in between the three a right angle triangle where the hypotenuse is the rectangle's diagonal:
![h^2+b^2=10^2=100](https://tex.z-dn.net/?f=h%5E2%2Bb%5E2%3D10%5E2%3D100)
So, we can use the equation : b + h = 14 to write one variable in terms of the other one and use it as substitution in the second (quadratic) equation:
h = 14 - b
then:
![h^2+b^2=100\\(14-b)^2+b^2=100\\14^2-28\,b+b^2+b^2=100\\2\,b^2-28\,b+196-100=0\\2\,b^2-28\,b+96=0\\b^2-14\,b+48=0](https://tex.z-dn.net/?f=h%5E2%2Bb%5E2%3D100%5C%5C%2814-b%29%5E2%2Bb%5E2%3D100%5C%5C14%5E2-28%5C%2Cb%2Bb%5E2%2Bb%5E2%3D100%5C%5C2%5C%2Cb%5E2-28%5C%2Cb%2B196-100%3D0%5C%5C2%5C%2Cb%5E2-28%5C%2Cb%2B96%3D0%5C%5Cb%5E2-14%5C%2Cb%2B48%3D0)
which we have reduced at the end by dividing both sides by 2.
we can use factoring to solve these equation;
![b^2-14\,b+48=0\\b^2-6\,b-8\,b+48=0\\b\,(b-6)-8\,(b-6)=0\\(b-6)\,(b-8)=0](https://tex.z-dn.net/?f=b%5E2-14%5C%2Cb%2B48%3D0%5C%5Cb%5E2-6%5C%2Cb-8%5C%2Cb%2B48%3D0%5C%5Cb%5C%2C%28b-6%29-8%5C%2C%28b-6%29%3D0%5C%5C%28b-6%29%5C%2C%28b-8%29%3D0)
Se we find two possible solutions: b = 6 m or b = 8 m
If we call b = 8 m, then the height becomes h = 14 - (8) = 6 m
and viceversa.
So a rectangle with such dimensions will render an area that equals :
Area = b x h = 8 x 6 = 48 square meters.
(a) - 5
since y varies inversely as x then k = yx ( k is the constant of variation )
using y = 5 when x = - 1, then k = 5 × - 1 = - 5
The standard form of the equation is 2x^2+16x+11
Answer for Problem 2:
x=61 degrees
Step-by-step explanation:
I'm not completely sure of problem 1, but I know what problem 2 is.
Tip: triangles always add up to 180 degrees.
1. 16+42= 58
2. 180-58= 122
3. 122 divided by 2= 61 degrees
ANSWER: x=61 degrees.
If any team is duplicated in the result (occurs more than once), do not include that result in the final data.