Question

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?

Answer 1

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 ,

$\longrightarrow A = x^2-14x+24$

And the base of the parallelogram is given by,

$\longrightarrow Base = x-2$

Substituting the values in the given formula, we have;

$\longrightarrow Area = base \times height$

$\longrightarrow x^2-14x+24=h(x-2)$

Divide both sides by (x-2) .

$\longrightarrow h =\dfrac{x^2-14x+24}{x-2}$

Factorise the term in numerator,

$\longrightarrow h =\dfrac{x^2-12x-2x+24}{x-2}$

$\longrightarrow h =\dfrac{x(x-12)-2(x-12)}{x-2}$

$\longrightarrow h =\dfrac{(x-2)(x-12)}{x-2}$

Simplify,

$\longrightarrow \underline{\underline{ height= x-12}}$

This is the required answer!