Question

1. The length of a rectangle is 6 mm longer than its width. Its perimeter is 32 mm. Let w equal the width of the rectangle.

a. Write an expression for the length in terms of the width.
b. Use expressions for the length and width to write an equation for the perimeter, on the basis of the given information.
c. Solve the equation, clearly indicating the width and length of the rectangle.

Answer 1

let
x-------> length of the rectangle
w-----> width of the rectangle

we know that
x=6+w

Part a) Write an expression for the length in terms of the width.
we have that
x=6+w----> this is an expression for the length in terms of the width.

Part b) Use expressions for the length and width to write an equation for the perimeter, on the basis of the given information.

P=32 mm
P=2*[x+w]
x=6+w
substitute the value of x in the perimeter formula
P=2*[6+w+w]
P=12+4w

the answer part b) is
P=12+4w

Part c) Solve the equation, clearly indicating the width and length of the rectangle.
P=12+4w
P=32
equate
12+4w=32
4w=32-12
4w=20
w=5 mm
remember that
x=6+w-----> x=6+5-----> x=11 mm

the answer part c) is
the length of the rectangle is 11 mm
the width of the rectangle is 5 mm