The perimeter of a rectangular is 58 cm. The length is 5 more than twice the width. Set up an expression for the length using w for width. Set up an equation to find the perimeter. Solve the equation to find the values of the length and the width (show your work)

Mathematics · College · Thu Feb 04 2021

llm

Answered on Mon Mar 07 2022

Given :

Perimeter of rectangle = 58cm

Length is 5 more than twice of its width

So, let the width (w) be x

Then, Length of rectangle would be 2x+5

Formula: perimeter of rectangle = 2(l+w)

Now, Substituting values, we get

58 = 2(2x+5+x)

Dividing both sides by 2, we get

58/2 = 2(3x+5)/2

29 = 3x + 5

3x = 24

Now, Dividing both sides by 3, we get

3x/x = 24/3

x = 8cm

So, width of rectangle is 8 cm.

Then, Length = 2(8) + 5

= 16 + 5

= 21cm

Hence, the Length and width of rectangle are 21 cm and 8 cm respectively.