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!!
