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the area of rectangle is x²+5x-36 sq. unit. its length and breadth is reduced by 2/2units. find new area of rectangle​

Sagot :

reinhard10158

Step-by-step explanation:

length × breadth = x² + 5x - 36

let's find, what expression was multiplied by what expression to give that result.

first we see, we have a pure x² term.

so, both start with (x + ...) or (x - ...).

then we see the last (constant) term -36.

so, we have a

(x + a)(x - b)

situation.

36 is the product of

6×6

9×4

12×3

18×2

the term +5x tells us that the difference between a and b must be 5. and a as the positive number must be bigger to give us the "+" (the multiplication contains "... + ax - bx ...").

and that means a = +9, b = -4

so, the original area calculation was

(x + 9)(x - 4) = x² + 5x - 36

when we decrease both factors by 2, we get

(x + 9 - 2)(x - 4 - 2) = (x + 7)(x - 6) = x² + x - 42

that is the new area of the rectangle.

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