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

x-12

Step by step 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 * height`

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

Divide both sides by (x-2) .

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

Factorise the term in numerator,

`\longrightarrow h =(x^2-12x-2x+24)/(x-2)\\`

`\longrightarrow h =(x(x-12)-2(x-12))/(x-2)\\`

`\longrightarrow h =((x-2)(x-12))/(x-2)`

Simplify,

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

This is the required answer!