Chapter 2: Introduction to Linear Polynomials
Chapter 2: Introduction to Linear Polynomials
Exercise
Question
Question: 7
11 / 11
11 / 11
If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?
SponsoredDesktop Banner
Answer
1
Let the width of the rectangle be x cm. Express the length using the given relationship.
Width = $x$ cm
Length = $(2x + 3)$ cm
2
Use the of the rectangle to find the width.Note: Perimeter of a rectangle = 2 × (length + width)
\text{2 × (Length + Width) = 24 $\quad$ ${color:#625b5f}[Perimeter of the rectangle = 24 cm]{/color}$}
⇒
\text{ $2 × (2x + 3 + x) = 24$ $\quad$ ${color:#625b5f}[Length = 2x + 3 and width = x]{/color}$}
⇒
$2 × (3x + 3) = 24$
⇒
$6x + 6 = 24$
⇒
$6x = 24 - 6$
⇒
$6x = 18$
⇒
\text{ $x = \dfrac{18}{6} = 3$ cm $\quad$ ${color:#625b5f}[Width]{/color}$}
3
Find the length.
$2x + 3$
⇒
\text{ $2 × {color:#2E2EFF}3{/color} + 3$}
⇒
$6 + 3$
⇒
\text{ 9 cm $\quad$ ${color:#625b5f}[Length]{/color}$}
4
Write the dimensions of the rectangle.
Answer: The width is 3 cm and the length is 9 cm.