Question

Question:-

The area of two similar triangles are 81 cm2 and 49 cm² respectively. If one of the sides of the first triangle is 6.3 cm, find the corresponding side of the other triangle.​

Answer 1

Explanation:

let's assume that the corresponding side of the second triangle is .

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

To find , we can solve the proportion above:

Taking the square root of both sides:

Simplifying the square root:

Cross-multiplying:

Dividing both sides by 9:

Calculating the value:

Therefore, the corresponding side of the second triangle is 4.9cm


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Answer 2

Let's assume that the corresponding side of the second triangle is
`\displaystyle\sf x`.

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

`\displaystyle\sf \left( (x)/(6.3) \right)^(2) =(49)/(81)`

To find
`\displaystyle\sf x`, we can solve the proportion above:

`\displaystyle\sf \left( (x)/(6.3) \right)^(2) =(49)/(81)`

Taking the square root of both sides:

`\displaystyle\sf (x)/(6.3) =\sqrt{(49)/(81)}`

Simplifying the square root:

`\displaystyle\sf (x)/(6.3) =(7)/(9)`

Cross-multiplying:

`\displaystyle\sf 9x = 6.3 * 7`

Dividing both sides by 9:

`\displaystyle\sf x = (6.3 * 7)/(9)`

Calculating the value:

`\displaystyle\sf x = 4.9`

Therefore, the corresponding side of the second triangle is
`\displaystyle\sf 4.9 \, cm`.

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