Select the correct answer from each drop-down menu.
The sides of ABC are 30 units, 40 units, and 60 units long. The corresponding sides of AXYZ are r times as long
as the sides of AABC.
2. If the area of AABC is n square units, the
The expression that gives the perimeter of AXYZ is
area of AXYZ is
square units.
Answers
Answer:
Area of ΔXYZ = n(r * r) square units
Step-by-step explanation:
Sides of ΔABC are 30 units, 40 units and 60 units.
Corresponding sides of another triangle XYZ are r times as long as the sides of ΔABC.
Therefore, sides of ΔXYZ will be, 30r units, 40r units and 60r units.
Perimeter of the triangle XYZ = 30r + 40r + 60r
= 130r units
If the area of ΔABC = n square units
Then the ratio of the area of ΔXYZ and ΔABC = (Ratio of the sides of ΔXYZ and ΔABC)²
[tex]\frac{\text{Area of triangle XYZ}}{\text{Area of triangle ABC}}=(\frac{\text{Side length of XYZ}}{\text{Side length of triangle ABC}})^2[/tex]
[tex]\frac{\text{Area of triangle XYZ}}{n}=(r)^2[/tex]
Area of ΔXYZ = nr² ≈ n(r * r)
Therefore, Option (3) will be the answer.
The expression that gives the perimeter of ΔXYZ is: 130r
The area of ΔXYZ = nr²
Similar FiguresIf A and B, with sides a and b respectively, are similar figures, therefore: area of A/area of B = a²/b².
Thus;
Given that the sides of ΔABC, which are 30, 40 and 60, are r times the corresponding sides of ΔXYZ, the sides of XYZ would be:
30r, 40r, 60r.
Perimeter of ΔXYZ = 30r + 40r + 60r = 130r
Given that the area of ΔABC is n units², therefore:
(area of ΔABC)/(area of ΔXYZ) = (side of ΔABC)²/(side of ΔXYZ)²
Substitute(n)/(area of ΔXYZ) = (30)²/(30r)²
n/area of ΔXYZ = 1/r²
Cross multiplynr² = area of ΔXYZ
area of ΔXYZ = nr²
Therefore, the expression that gives the perimeter of ΔXYZ is: 130r
The area of ΔXYZ = nr²
Learn more about area of similar figures on:
https://brainly.com/question/26145340
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