the area formula is a parallelogram is equal to (Base)*(height). If the area if a parallelogram is given by the trinomial x^2-14x+24. The base of parallelogram is (x-2), what is an expression for the height of the parallelogram?

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VirαtKσhli VirαtKσhli · Answer 1 · 2022-02-26T05:22:43+01:00

Answer:

x-12

Step by step explanation:

Here it is given that the area of a parallelogram is given by base * height. And if the area is represented by ,

[tex]\longrightarrow A = x^2-14x+24[/tex]

And the base of the parallelogram is given by,

[tex]\longrightarrow Base = x-2 [/tex]

Substituting the values in the given formula, we have;

[tex]\longrightarrow Area = base \times height [/tex]

[tex]\longrightarrow x^2-14x+24=h(x-2)\\ [/tex]

Divide both sides by (x-2) .

[tex]\longrightarrow h =\dfrac{x^2-14x+24}{x-2}[/tex]

Factorise the term in numerator,

[tex]\longrightarrow h =\dfrac{x^2-12x-2x+24}{x-2}\\[/tex]

[tex]\longrightarrow h =\dfrac{x(x-12)-2(x-12)}{x-2}\\ [/tex]

[tex]\longrightarrow h =\dfrac{(x-2)(x-12)}{x-2} [/tex]

Simplify,

[tex]\longrightarrow \underline{\underline{ height= x-12}} [/tex]

This is the required answer!