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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.

Select the correct answer from each dropdown menu The sides of ABC are 30 units 40 units and 60 units long The corresponding sides of AXYZ are r times as long class=

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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.

akposevictor

The expression that gives the perimeter of ΔXYZ is: 130r

The area of ΔXYZ = nr²

Similar Figures

If 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 multiply

nr² = area of ΔXYZ

area of ΔXYZ = nr²

Therefore, the expression that gives the perimeter of ΔXYZ is: 130r

The area of ΔXYZ = nr²

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