The perimeter of a rectangular picture frame is 30 inches. The length of the frame is three inches less than twice the width. What are the dimensions of the frame?

Perimeter-30 in Length-2x-3 Width-x
P=2[l+w] 30=2[2x-3+x] 30=2[3x-3] 30=6x-6 Add 6 to both sides 36=6x Divide both sides by 6 x=6
Length:9 Width:6

Answered by HunterX | 2024-06-10

The **dimensions **are length equal to 9 inches and width equal to 6 inches.
It is given that length of rectangular frame is three less than twice the width and its** perimeter** is 30 inches.
We have to find out the dimensions of the frame .
What is the perimeter of a rectangle ?
The perimeter of a rectangle is 2 ( b + l ) , where b is width and **l **is the **length **of the rectangle.
As per the **question ; **
Length of rectangular frame is three less than twice the width.
Let's assume width be** x.**
So ;
**Length **will be ;
= 2x - 3
We know that ;
**Perimeter **of a **rectangle **is given by ;
P = 2 ( b + l )
⇒ 30 = 2 ( x + 2x - 3 )
⇒ 30 = 2 × ( 3x - 3 )
⇒ 30 = 6x - 6
⇒ 6x = 36
⇒** x = 6 inches **
So ;
width will be 6 inches and length will be ;
l = 2x - 3
l = 2 × 6 - 3
l = 12 - 3
length = 9 inches
Thus , the **dimensions **are length equal to 9 inches and width equal to 6 inches.
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Answered by psm22415 | 2024-06-16

The dimensions of the rectangular picture frame are a width of 6 inches and a length of 9 inches. This was determined by using the perimeter formula and the given relationship between length and width. By solving the equations step-by-step, we arrived at these dimensions.
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Answered by psm22415 | 2024-12-24