contestada

A square with an area of A2 is enlarged to a square with an area of 25A2. How was the side of the smaller square changed?

The side length was increased by 5.
The side length was multiplied by 5.
The side length was increased by 10.
The side length was multiplied by 10.

Respuesta :

reinhard10158

Answer:

second option : the side length was multiplied by 5.

Step-by-step explanation:

a = side length of the original square

A² = a×a

(a+5)×(a+5) = a² + 10a + 25

and that should be equal to a²×25

a² + 10a + 25 = 25a² ?

10a + 25 = 24a²

no, that is not true for all a

a×5 × a×5 = a²×25 = 25A²

this is the correct solution, as it is true for all a.

abidemiokin

For the area to be  25a², the side length was increased by 5.

How to calculate the area of a square

Let a be the side length of the original square, hence:

A = a²

Increasing the length by 5 will give:

(a+5)×(a+5) = a² + 10a + 25

Factorizing the result

a² + 10a + 25 = (a+5)²

a² + 10a + 25 = 25a²

This shows that for the area to be  25a², the side length was increased by 5.

Learn more on area of square here: https://brainly.com/question/25092270

Otras preguntas