Question

the length of a rectangle is 3 more than its width .if the perimeter of the rectangle is 30 cm then find the length and width of the rectangle​

Answer 1

Answer:

Given :-

• The length of a rectangle is 3 more than its width.
• The perimeter of a rectangle is 30 cm.

To Find :-

• What is the length and width of the rectangle.

Formula Used :-

♣ Perimeter Of Rectangle Formula ♣

★ Perimeter Of Rectangle = 2(L + W) ★

where,

• L = Length
• W = Width

Solution :-

Let,

➲ Width = a cm

➲ Length = (a + 3) cm

According to the question by using the formula we get,

⇒ 30 = 2{(a + 3) + a}

⇒ 30 = 2(a + a + 3)

⇒ 30 = 2(2a + 3)

⇒ 30 = 4a + 6

⇒ 30 - 6 = 4a

⇒ 24 = 4a

⇒ 24/4 = a

⇒ 6/1 = a

⇒ 6 = a

➠ a = 6 cm

Hence, the required length and width of a rectangle are :

❒ Length Of Rectangle :

↦ Length of Rectangle = (a + 3) cm

↦ Length of Rectangle = (6 + 3) cm

➦ Length of Rectangle = 9 cm

❒ Width Of Rectangle :

↦ Width Of Rectangle = a cm

➦ Width Of Rectangle = 6 cm

∴ The length and width of a rectangle is 9 cm and 6 cm respectively.

Answer 2

Given :-

• Length of the rectangle is 3 more than it's width
• Perimeter of the rectangle is 30 cm

To Find :-

• Length and width of the rectangle

$\sf \underline{Formula \: used \: \: \: } \\ \sf\blue{ Perimeter = 2 \times (length + breadth }$

↦Let the width of the rectangle be x

↦Therefore, its length = x + 3cm

Now, putting the values, we get :-

$\sf \red{\implies \: 2(x + x + 3) = 30cm} \\ \sf \pink{\implies \:2(2x + 3) = 30 \: cm \: \: \: \: } \\ \sf \blue{\implies \:4x + 6 = 30 \: cm \: \: \: \: \: \: \: \: \: \: } \\ \sf \gray{\implies \: 4x = 30 \: cm - 6 \: cm \: \: \: } \\ \sf \green{\implies \:x = \frac{ \cancel{24}}{ \cancel4} = 6 \: cm \: \: \: \: \: \: \: \: \: \: }$

$\sf \therefore \: length \: = x + 3 \: cm = 6 + 3 = 9 \: cm \\ \sf \: and \: width \: = x \: = 6 \: cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

VERIFICATION :-

Putting the values of length and width in the formula of Perimeter, we get,

$\sf \longrightarrow \: 2(6 + 9) = 30 \: cm \\ \sf \longrightarrow 2 \: \times \: 15 = 30 \: \: cm \\ \sf \longrightarrow 30 \: cm \: = 30 \: cm \: \: \: \\ \sf\therefore L.H.S. = R.H.S \: \: \: \: \: \: \\ </p><p>\sf {Hence \: , \: verified \: \: \: \: \: \: \: \: }$