Question

give possible expressions for the length and breadth of rectangle whose area is 25 x square + 30 X square + 9 x square - 4 Z Square​

Answer 1

Length = 8x + 2z

Breadth = 8x - 2z

Step-by-step explanation:

Given expression for area of rectangle

= $25x^2 + 30x^2 + 9x^2 - 4z^2$

= $64x^2 - 4z^2$

= $(8x)^2 - (2z)^2$

= (8x + 2z)(8x - 2z)...........(1)    [$a^2 - b^2 =(a+b)(a-b)$]

We know that Area of rectangle = length × breadth.....(2)

On comaparing equation (1) and (2)

Length = 8x + 2z

Breadth = 8x - 2z

Answer 2

Length=$8x+2z$

Breadth=$8x-2z$

Step-by-step explanation:

Given area of rectangle :

$25x^2+30x^2+9x^2-4z^2$

Combine like terms , then we get

$64x^2-4z^2$

$(8x)^2-(2z)^2$

$Identity:a^2-b^2=(a+b)(a-b)$

By using this identity

Then, we get

$(8x+2z)(8x-2z)$

We know that

Area of rectangle :$Length\times breadth$

By comparing we get

Length of rectangle =$8x+2z$

Breadth of rectangle=$8x-2z$

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