Question

The perimeter of a rectangle is 78cm.
Its longest side has a length of 22cm.
State the length of the shortest side

Answer 1

Given -

• Perimeter of rectangle = 78m

• Length of longest side = 22cm

To find -

• Length of shortest side.

Formula used -

• $\sf \: \dfrac{p}{2} - l$

Solution -

In the question, we are provided with the perimeter of a rectangle, and with it's longest side, and we need to find it's shortest side, for that we will use the formula of perimeter of rectangle, and we will put all the values together, then we will solve the whole problem. Let's do it!

According to question -

Let the length of shortest side be b

Length of longest side is 22cm

Perimeter is 78cm

So -

Perimeter of rectangle = 2(l + b)

where -

l = Length = 22cm

b = Breadth = b cm

On substituting the values -

$\sf \longrightarrow\: p = 2(l \: + \: b) \\ \\ \\ \sf \longrightarrow \: 78cm = 2(22 \: + \: b) \\ \\ \\ \sf \longrightarrow\: b = \dfrac{78}{2} - 22 \\ \\ \\ \sf \longrightarrow \: b \: = \cancel \dfrac{78}{2} - 22 \\ \\ \\ \sf \longrightarrow\: b = 39 - 22 \\ \\ \\ \sf \implies\: b = 17cm$

$\therefore$ The shortest length is 17cm

Verification -

$\sf \: p = 2(l \: + \: b) \\ \\ \sf \: 78cm = 2(22 \: + \: 17) \\ \\ \sf \: 78cm = 2(39) \\ \\ \sf \: 78cm = 78cm$

__________________________________________________

Answer 2

$\; \; \; \; \; \;{\large{\bold{\sf{\underbrace{\underline{Understanding \; the \; question}}}}}}$

➳ This question says that the perimeter of the rectangle is 78 cm. It's longest side's length is 22 cm and we have to find the length of it's shortest sides.

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 22 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 17 cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

$\; \; \; \; \; \; \; \; \; \;{\large{\bold{\sf{\underline{Given \; that}}}}}$

➳ Perimeter of rectangle = 78 cm.

➳ Longest side length = 22 cm.

$\; \; \; \; \; \; \; \; \; \;{\large{\bold{\sf{\underline{To \; find}}}}}$

➳ Length of it's shortest side.

$\; \; \; \; \; \; \; \; \; \;{\large{\bold{\sf{\underline{Solution}}}}}$

➳ Length of it's shortest side = 17 cm

$\; \; \; \; \; \; \; \; \; \;{\large{\bold{\sf{\underline{Using \: concept}}}}}$

➳ Perimeter of rectangle formula

$\; \; \; \; \; \; \; \; \; \;{\large{\bold{\sf{\underline{Using \: formula}}}}}$

➳ Perimeter of rectangle = 2(l+b)

$\; \; \; \; \; \; \; \; \; \;{\large{\bold{\sf{\underline{Where,}}}}}$

➳ l denotes length

➳ b denotes breadth

$\; \; \; \; \; \; \; \; \; \;{\large{\bold{\sf{\underline{Full \; Solution}}}}}$

~ According to the question,

$\sf Given \; that \: and \: to \: find \begin{cases} & \sf{Perimeter \: of \: rectangle = \: \bf{78 \: cm}} \\ & \sf{L \: of \: longest \: side = \: \bf{22 \: cm}} \\ & \sf{L \: of \: shortest \: side = \: \bf{?}} \end{cases}$

~ Finding the length of shortest side of that rectangle

Using formula to find perimeter of rectangle

➨ Perimeter of rectangle = 2(l+b)

$\; \; \; \; \; \; \; \; \; \;{\large{\bold{\sf{\underline{Here,}}}}}$

➳ Perimeter is 78 cm

➳ Length is 22 cm

➳ Breadth is ?

~ Putting the values

➨ Perimeter of rectangle = 2(l+b)

➨ 78 = 2(22+b)

➨ 78 = 44 + 2b

➨ 78 - 44 = 2b

➨ 34 = 2b

➨ 34/2 = b

➨ 17 = b

➨ b = 17 cm

${\pink{\frak{Breadth \: measure \: 17 \: cm}}}$

$\; \; \; \; \; \; \; \; \; \; \; \; \; \;{\bold{\rm{Or}}}$

${\pink{\frak{Henceforth, \: length \: of \: shortest \: side \: of \: rectangle \: is \: 17 \: cm}}}$

$\; \; \; \; \; \; \; \; \; \;{\large{\bold{\sf{\underline{Knowledge \; booster}}}}}$

Rectangle diagram -

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large x cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large y cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

Area of rectangle formula -

Area of rectangle = L × B

Perimeter of rectangle formula -

Perimeter of rectangle = 2(l+b)

Diagram of this question -

Kindly see from attachment or see below where I tell question meaning.