Question

What fraction of the rectangle is shaded? Write your answer as a rational expression in simplified form.

Answer 1

How do you find the area of the triangle?

Answer 2

i actually don't rememeber the formula

Answer 3

Area of a triangle = (base*height)/2

A = (bh)/2

Does that help?

Answer 4

ok and how do i do that with letters?

Answer 5

First calculate the area of the triangle


A = (bh)/2

A = (x*2)/2

A = 2x/2

A = x


So the area of the triangle is x square units. Making sense so far?

Answer 6

yes

Answer 7

Now calculate the area of the rectangle

A = LW

A = (x+2)x

A = x^2+2x

So the area of the rectangle is x^2+2x square units.

Answer 8

So what's next?

Answer 9

ummm i have no idea im trying to follow

Answer 10

The next step is to divide the area of the triangle into the area of the rectangle, so...


(Area of triangle)/(Area of rectangle) = (x)/(x^2+2x)


Now simplify


(x)/(x^2+2x)

(x)/(x(x+2))

1/(x+2)


So the fraction that's shaded is 1/(x+2)

Answer 11

This fraction may be a bit odd, but say x is 2

This would mean that the fraction that's shaded is 1/(x+2) = 1/(2+2) = 1/4

So when x = 2, the shaded triangle takes up a quarter of the rectangle

Answer 12

can u help mye with my next question?>

Answer 13

sure

Answer 14

((4x+12)/^2-2x)) * ((x)/(6x+18))

Answer 15

is it ((4x+12)/(x^2-2x)) * ((x)/(6x+18)) ?

Answer 16

Think you meant to say x^2 instead of ^2

Answer 17

of yes

Answer 18

((4x+12)/(x^2-2x))*((x)/(6x+18))


((4x+12)*(x))/((x^2-2x)*(6x+18))


(x(4x+12))/((x^2-2x)*(6x+18))


(x(4x+12))/(x(x-2)*(6x+18))


(4x(x+3))/(x(x-2)*(6x+18))


(4x(x+3))/(x(x-2)*6(x+3))


(4x(x+3))/(6x(x-2)(x+3))


(2)/(3(x-2))


(2)/(3x-6)


So the final answer is \[\Large \frac{2}{3x-6}\]

Answer 19

a^2 = 5a + 4 / a^3 * a^2 + 3a = 2 / a^2 - 2a

Answer 20

are those equal signs supposed to be + signs?