Question

If the ratio of areas of two similar triangles ABC and COD is 1:4 then which of the following statements is true?
a. The ratio of their perimeter is 3:4
b. The corresponding altitude have a ratio 1:2
c. The medians have a ratio 1:4
d. The angle bisectors have a ratio 1:16​

Answer 1

Answer:

A is the true answer

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Answer 2

If  ratio of areas of two similar triangles is 1 : 4 then  The corresponding altitude have a ratio 1:2

Given:

• ΔABC ~ ΔCOD
• ratio of areas is 1:4

To Find:

• Choose correct option:
• a. The ratio of their perimeter is 3:4
• b. The corresponding altitude have a ratio 1:2
• c. The medians have a ratio 1:4
• d. The angle bisectors have a ratio 1:16​

Solution:

Concept/Formulas to be used:

Ratio of perimeter of Similar triangle is same as Ratio of corresponding sides

Ratio of Area of Similar triangle is square of Ratio of corresponding sides

Ratio of Median of Similar triangle is same as Ratio of corresponding sides

Ratio of Altitude of Similar triangle is same as Ratio of corresponding sides

Ratio of angle bisectors of Similar triangle is same as Ratio of corresponding sides

Step 1:

Use formula Ratio of Area of Similar triangle is square of Ratio of corresponding sides to find ratio of corresponding sides

=> (ratio of corresponding sides)² = 1/4

=> ratio of corresponding sides = 1/2

Step 2:

Use formula for Ratio of Altitude of Similar triangle is same as Ratio of corresponding sides

Hence The corresponding altitude have a ratio 1:2

option b) is correct

Step 3:

Use formula for Ratio of perimeter of Similar triangle is same as Ratio of corresponding sides

Hence  ratio of their perimeter is 1:2

option a) is incorrect

Step 4:

Use formula for Ratio of Median of Similar triangle is same as Ratio of corresponding sides

Hence The corresponding Medians have a ratio 1:2

option c) is incorrect

Step 5:

Use formula for Ratio of  angle bisectors of Similar triangle is same as Ratio of corresponding sides

Hence The corresponding  angle bisectors have a ratio 1:2

option d) is incorrect

If  ratio of areas of two similar triangles is 1 : 4 then  The corresponding altitude have a ratio 1:2

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