The perimeter of a rectangle is 310 m. The length is 25 m greater than the width. What are the length and the width of this rectangle?
Answers
Width: 65 m
Length: 90 m
Explanation:
The perimeter of a reactangle is given by the formula
P
=
2
⋅
(
w
+
L
)
, where
w
- the width of the rectangle;
L
- the length of the rectangle.
You know that the length of the rectangle is 25 m greater than it width. In other words, if you add 25 meters to the rectangle's width, you get its length.
This can be written as
L
=
w
+
25
The perimeter will be equal to
P
=
2
⋅
⎡
⎢
⎣
w
+
(
w
+
25
)
=L
⎤
⎥
⎦
P
=
2
⋅
(
w
+
w
+
25
)
=
2
⋅
(
2
w
+
25
)
=
4
w
+
50
This means that the width of the rectangle will be
4
w
=
P
−
50
=
310
−
50
=
260
w
=
260
4
=
65 m
The length of the rectangle will be
L
=
w
+
25
=
65
+
25
=
90 m
Check to see if the values you got are correct
P
=
2
⋅
(
65
+
90
)
=
2
⋅
155
=
310
→
the two values are valid!
perimeter of rectangle = 2×L+B
Length =x+25
length = x
2×(x+x+25)
2×(2x+25)=310
4x+50=310
4x=260
x=65