Answer:
width = 4 in
length = 9 in
Step-by-step explanation:
To solve this problem, write an expression for the length and use the area of a rectangle formula.
The formula for area of a triangle is A = lw
"A" is the area.
"l" is the length.
"w" is the width.
"The length of a rectangle is 5 more than the width". It is represented in an expression:
l = w + 5 The width plus 5 is the length.
We also know the area is 36 in². Using information we know, replace variables in the formula for area of a rectangle.
Substitute l = w + 5 and A = 36
A = lw
36 = (w + 5)w Expand by multiplying w by the terms in the brackets.
36 = w² + 5w Since the equation is quadratic, make it equate to 0.
36 - 36 = w² + 5w - 36 Subtract 36 from both sides
0 = w² + 5w - 36 Factor this. Use group factoring, which is when you replace the middle term (5w) with two terms that add to make 5w, and multiply to get the last term (-36).
0 = w² + 9w - 4w - 36 9w times -4w is -36. They also add to get 5w.
0 = (w² + 9w) + (-4w - 36) Group the factors
0 = w(w + 9) + -4(w + 9) Take out the common factor in each group.
0 = w(w + 9) + -4(w + 9) Take out the new common factor binomial w+9
0 = (w + 9) (w - 4) Fully factored equation.
w + 9 = 0 w - 4 = 0 Set each binomial to equal 0.
w = -9 w = 4 Chose what makes sense to be the width.
The width cannot be a negative number, so the width is 4.
Since we know the width, we can find the length because the length is 5 more than the width.
l = w + 5
l = 4 + 5
l = 9 Length of the rectangle
Don't forget to include the units, inches.
Therefore the length is 9 inches and the width is 4 inches.
means that you should take points with y-coordinates greater than or equal to 2 (top part of the coordinate plane that was formed by the red line);
means that you should take points with x-coordinates less than or equal to 6 (left part of the coordinate plane that was formed by the blue line);
you can check where the origin is placed. Since
, the origin belongs to the needed part and you have to take the right part of the coordinate plane that was formed by green line.
you can check where the origin is placed. Since
, the origin belongs to the needed part and you have to take the bottom part of the coordinate plane that was formed by orange line.
