Question

The perimeter of the rectangle is ${16}^{\prime \prime }.$ The length of the rectangle is one less than two times its height. What are the dimensions of the rectangle?

• A. $4^{\prime \prime }$ and $4^{\prime \prime }$
• B. $5^{\prime \prime }$ and $3^{\prime \prime }$
• C. $3^{\prime \prime }$ and $2^{\prime \prime }$
• D. $7^{\prime \prime }$ and $4^{\prime \prime }$

Answer 1

The correct option is B $5^{\prime \prime }$ and $3^{\prime \prime }$

Let the length and height of the rectangle are $x$ and $y$ respectively,


then according to the given conditions
Perimeter $=16$
$\Rightarrow x+y+x+y=16\Rightarrow 2x+2y=16$
Dividing both the sides by $2,$ we get
$\Rightarrow x+y=8\dots \left(i\right)$

and the length of the rectangle is one less than two times its height
$\therefore x=2y-1$
$\Rightarrow x-2y=-1\dots \left(ii\right)$

Step 1: Find the value of y
$\left(i\right)-\left(ii\right)\Rightarrow (x+y)-(x-2y)=8-(-1)$
$\Rightarrow y+2y=8+1\Rightarrow 3y=9$
Dividing both the sides by $3,$ we get
$\Rightarrow y=3$

Step 2: Find the value of x
Putting $y=3$ in $\left(i\right),$ we get
Equation $\left(i\right)\to x+\left(y\right)=8$
$x+3=8$
subtracting by $3$ on both sides
$\Rightarrow x=8-3=5$
$\therefore x=5,y=3$
Hence, dimensions of the rectangle are $5^{\prime \prime }$ and $3^{\prime \prime }.$