The length of a rectangle is 3 1/6 cm longer than the width. The perimeter of the rectangle is 15 1/3 cm. What are the width and

Question

BartSMP [9]

3 years ago

6

The length of a rectangle is 3 1/6 cm longer than the width. The perimeter of the rectangle is 15 1/3 cm. What are the width and

length of this rectangle?

Mathematics

1 answer:

ahrayia [7] · Answer 1 · 2022-05-15T16:01:41+03:00

The width of rectangle is $2\frac{1}{4}$ cm and length is $5\frac{5}{12}$ cm.

Step-by-step explanation:

Let,

Width of rectangle = w

Length of rectangle = $w+3\frac{1}{6}=w+\frac{19}{6}$

Perimeter of rectangle = $15\frac{1}{3}=\frac{46}{3}$ cm

Perimeter = 2(Length + Width)

$\frac{46}{3}=2(w+\frac{19}{6}+w)\\\\\frac{46}{3}=2(2w+\frac{19}{6})\\\\\frac{46}{3}=4w+\frac{19}{3}\\\\4w+\frac{19}{3}=\frac{46}{3}\\\\4w=\frac{46}{3}-\frac{19}{3}\\\\\ 4w=\frac{46-19}{3}\\\\4w=\frac{27}{3}\\\\4w=9$

Dividing both sides by 4

$\frac{4w}{4}=\frac{9}{4}\\\\w=\frac{9}{4}$

Width of rectangle = $\frac{9}{4}=2\frac{1}{4}\ cm$

$Length = w+\frac{19}{6}=\frac{9}{4}+\frac{19}{6}\\\\Length = \frac{27+38}{12}=\frac{65}{12}\\\\Length=5\frac{5}{12}\ cm$

The width of rectangle is $2\frac{1}{4}$ cm and length is $5\frac{5}{12}$ cm.

Keywords: rectangle, perimeter

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