Question

give possible expressions for the length and breadth of the each of the following rectangles, in which their area is m^2+14m+40​

Answer 1

Given that :

The area of the rectangle = m^2 + 14m + 40

To find :

Length and Breadth of the rectangle.

As we know that :

Area of a rectangle = Length × Breadth .... (1)

On factoring the following expression

m^2 + 14m + 40

=> m^2 + 10m + 4m + 40

=> m(m + 10) + 4(m + 10)

=> (m + 10)(m + 4) ... (2)

From equation (1) and (2) :

Length of the 1st rectangle = (m + 10)

And Breadth of the 2nd rectangle = (m + 4)

Also, Length of the 2nd rectangle = (m + 4)

and Breadth of the 2nd rectangle = (m + 10)

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Hope it helps ☺