Can someone help me with this
1 answer:
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Answer:
The perimeter of triangle ΔABC is approximately;
(A) 20.0
Step-by-step explanation:
In ΔABC, the coordinates of the vertices are given as follows;
A(-4, 1), B(-2, 3), C(3, -4)
The length, 'l', of the sides of the triangle with known 'x', am]nd 'y' coordinates are given as follows;
Therefore, we have;
The length of segment = √((3 - 1)² + (-2 - (-4))²) = 2·√2 ≈ 2.83
The length of segment = √(((-4) - 3)² + (3 - (-2))²) = √74 ≈ 8.6
The length of segment = √(((-4) - 1)² + (3 - (-4))²) = √74 ≈ 8.6
The perimeter of a geometric shape is equal to the sum of the length of sides of the figure
The perimeter of triangle ΔABC = (The length of segment ) + (The length of segment
) + (The length of segment
)
∴ The perimeter of triangle ΔABC = 2·√2 + √74 + √74 ≈ 20.0.
Answer:
The volume of the geometric solid produced is 391 cubic cm ⇒ A
Step-by-step explanation:
<em>When a </em><em>right triangle is rotated about its vertical leg 360°</em><em>, then it formed </em><em>a cone</em><em> its radius is the horizontal leg of the triangle and its height is the vertical lege of the triangle.</em>
The rule of the volume of the cone is V = π r² h, where
- r is the radius of its base
- h is the length of its height
∵ Triangle XYZ is rotated 360° about the vertical side YZ
∴ It formed a cone with a radius = XZ and a height = YZ
∵
∵ YX = 6√3
∴
∵ tan(60) = √3
∴ = √3
→ By using cross multiplication
∴ 6√3 = XZ(√3)
→ Divide both sides by √3
∴ 6 = XZ
∵ XZ = r and YZ = h
∴ r = 6 and h = 6√3
→ By using the rule of the cone above
∵ V = (π) (6)² (6√3)
∴ V ≅ 391 cm³
∴ The volume of the geometric solid produced is 391 cubic cm