Question

David has a rectangle and a right triangle.
The length of the rectangle is 5 more than its width, W.
The length of the shorter leg of the triangle is equal to the rectangle's
width.
The length of the longer leg of the triangle is twice the length of the
rectangle.
Which function, f(w), represents the combined area of the rectangle and the
triangle?

Answer 1

Answer:

2w^2+10w

Step-by-step explanation:

Let's start with the rectangle.

The length of the rectangle is:

L = 5 + w

The width of the rectangle is:

W

So, the equation of the area for the rectangle would be:

(w)(5+w) due to the area of a rectangle being length x width

Now, onto the triangle.

The length of the shorter side is equal to the width of the rectangle:

L(1) = w

The length of the longer side of the triangle is twice the length of the rectangle, so going back to what we have the rectangles length being:

L(2) = (2)(5+w) or 10 + 2w

Now to find the area of the triangle, use the equation 1/2(b)(height)

So plug it in:

1/2(w)(10 + 2w)

Which equals 1/2(10w + 2w^2)

Now, we times it by 1/2, so we will put it into a fraction:

1 x (10w + 2w^2)/2

10w + 2w^2/2

Now factor it:

2w(5 + w)/2

2 cancels out 2, so we are left with

w(w+5) = w^2 + 5w

So, the equation says what is the combined area of the rectangle and triangle

Rectangle area: w(w+5) = w^2 + 5w

Triangle area: w^2 + 5w

So, the combined area is 2w^2 + 10w

hope that helps!! I understand this question is hard, so I tried to explain as best as I can :)

for me, this is an EOC question, so to all those taking the test good luck! study hard!!