Answer:
80 yd^2
Step-by-step explanation:
Since the formula for squares is s^2, we can use this to set up an equation, which is
s^2=400
If we square root this, we get
s=20
The perimeter formula for a square is 4s, so if we plug in, we end up with 80 yd^2
If two similar triangles have sides in the ratio a : b, then their areas are in the ratio a² : b².
We have the ratio:
![54:18=\dfrac{54}{18}=3:1](https://tex.z-dn.net/?f=54%3A18%3D%5Cdfrac%7B54%7D%7B18%7D%3D3%3A1)
Area of the smaler triangle = x
Area of the larger triangle = 567 cm²
Therefore we have the equation:
![567:x=3^2:1^2\\\\\dfrac{567}{x}=\dfrac{9}{1}\qquad|\text{cross multiply}\\\\9x=567\qquad|\text{divide both sides by 9}\\\\x=63](https://tex.z-dn.net/?f=567%3Ax%3D3%5E2%3A1%5E2%5C%5C%5C%5C%5Cdfrac%7B567%7D%7Bx%7D%3D%5Cdfrac%7B9%7D%7B1%7D%5Cqquad%7C%5Ctext%7Bcross%20multiply%7D%5C%5C%5C%5C9x%3D567%5Cqquad%7C%5Ctext%7Bdivide%20both%20sides%20by%209%7D%5C%5C%5C%5Cx%3D63)
<h3>Answer: C. 63 cm²</h3>
<h3>
Answer: 130</h3>
Explanation:
Let x be the unknown angle we want to find.
Let y be adjacent and supplementary to x. This means x+y = 180
Let z also be adjacent and supplementary to x. So x+z = 180 also
Subtracting the two equations leads to y-z = 0 and y = z. So effectively we've proven the vertical angle theorem.
Since the supplementary angles to x add to 100, we know that y+z = 100. Plug in y = z and solve for z
y+z = 100
z+z = 100
2z = 100
z = 100/2
z = 50
Therefore,
x+z = 180
x+50 = 180
x = 180-50
x = 130
Yeah it looks like it’s right
Answer:
25
Step-by-step explanation:
As the triangles within the bigger triangle are similar, the sides are in proportion.
⇒ ![\frac{18}{30} = \frac{15}{w}](https://tex.z-dn.net/?f=%5Cfrac%7B18%7D%7B30%7D%20%3D%20%5Cfrac%7B15%7D%7Bw%7D)
⇒ ![\frac{3}{5} = \frac{15}{w}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B5%7D%20%3D%20%5Cfrac%7B15%7D%7Bw%7D)
⇒ 3w = 75
⇒ w = 25