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.
, we can use this to find the height of the lamp along with the information that the total distance from the lamp to the tip of his shadow is 20:
