Answer:
The answer to your question is z = ![\sqrt{24}](https://tex.z-dn.net/?f=%5Csqrt%7B24%7D)
Step-by-step explanation:
Process
I'll solve this problem using proportions, I hope it helps you
We consider the adjacent side of both triangle
Adjacent side small triangle = x Adjacent side big triangle = 10
Proportion of these sides = ![\frac{x}{10}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B10%7D)
Now, consider the opposite side of both triangles
Opposite side fo small triangle = 2 Opposite side big triangle = x
Proportion = ![\frac{2}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7Bx%7D)
Now, equal both proportions and solve for x
![\frac{x}{10} = \frac{2}{x}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B10%7D%20%3D%20%5Cfrac%7B2%7D%7Bx%7D)
x² = 20
x = ![\sqrt{20}](https://tex.z-dn.net/?f=%5Csqrt%7B20%7D)
x = 2
Using Geometric mean
x = ![\sqrt{2x10} = \sqrt{20}](https://tex.z-dn.net/?f=%5Csqrt%7B2x10%7D%20%3D%20%5Csqrt%7B20%7D)
Using the Pythagorean theorem to find z
z² = (√20)² + 2²
z² = 20 + 4
z² = 24
z = ![\sqrt{24}](https://tex.z-dn.net/?f=%5Csqrt%7B24%7D)
Remark
Break them into small figures: triangle, square ( I presume), and a parallelogram.
Triangle
<u>Formula</u>
A = 1/2 * b * h
<u>Givens</u>
b = 7
h = 4
<u>Solve</u>
Area = 1/2 b*h = 1/2 * 7 * 4 = 14
Square
<u>Formula</u>
Area = s^2
<u>Solve</u>
s = 7
Area = 7^2 = 49
Parallelogram
<u>Formula</u>
A = b*h
<u>Givens</u>
b = 7
h = 3
<u>Solve</u>
Area = 7 * 3
Area = 21
Total Area
Total Area = triangle + Square + Parallelogram
Total Area = 14 + 49 + 21 = 84 square yards.
2x-3y=1
+2x+3y=2
4x=3 substitute 3/4 for x in the first equation..you get y=2/9.
x=3/4
Hello from MrBillDoesMath!
Answer:
12 sqrt(2)
Discussion:
Since we have a right triangle,
cos(45) = side adjacent/ hypotenuse
= 12/ c
As cos(45) = sqrt(2)/2 the above equation becomes
sqrt(2)/2 = 12/c => multiple each side by "c"
c sqrt(2)/2 = 12/c * c =>
c sqrt(2)/2 = 12 => divide both sides by sqrt(2)/2
c = 12/ (sqrt(2)/2) =>
c = 12 *2 / sqrt(2) => as 2/sqrt(2) = sqrt(2)
c = 12 sqrt(2)
which is the first answer provided.
Thank you,
MrB