Question

the breadth of the rectangle is 16m less than its length .The perimeter of the rectangle
is 480m. Find the area of the rectangle​

Answer 1

$\large\sf\underline{Given\::}$

• The breadth of the rectangle is 16 m less than it's length.

• Perimeter of the rectangle = 480 m

‎

$\large\sf\underline{To\:find\::}$

• Area of the rectangle

‎

$\large\sf\underline{How\:to\:do\:?}$

Here in this question we are given that the breadth of the rectangle is 16 less than it's length . Assuming length to be x m . Breadth would be 16 less than x i.e., (x - 16) m . We are also given the perimeter of the rectangle as 480 m . So we would frame an equation from the formula of perimeter and the given value. Solving the equation we would get the measure of length and breadth of the rectangle . Then finally we could use the formula for area of rectangle and get our final answer. Let's begin !

‎

$\large\sf\underline{Assumption\::}$

Let :

• The length of the rectangle be x m.

• The breadth would be (x - 16) m.

‎

$\large\sf\underline{Formula\:to\:be\:used\::}$

• Perimeter of the rectangle = $\sf\:2(l+b)$

• Area of the rectangle = $\sf\:length \times breadth$

‎

$\large\sf\underline{Solution\::}$

We know :

Perimeter of rectangle = 2 (l + b) ---(i)

According to the question :

Perimeter of the rectangle = 480 m ---(ii)

So equating (i) and (ii) :

$\sf\rightarrow\:2(l+b) =480$

• Substituting the assumed value of l and b

$\sf\rightarrow\:2[x+(x-16) ]=480$

$\sf\rightarrow\:2[x+x-16 ]=480$

$\sf\rightarrow\:2[2x-16 ]=480$

• Multiplying and removing the brackets

$\sf\rightarrow\:4x-32=480$

• Transposing -32 to other side it becomes +32

$\sf\rightarrow\:4x=480+32$

$\sf\rightarrow\:4x=512$

• Transposing 4 to other side it goes to the denominator

$\sf\rightarrow\:x=\frac{512}{4}$

• Reducing it to lower terms

$\sf\rightarrow\:x=\cancel{\frac{512}{4}}$

$\small{\underline{\boxed{\mathrm\red{\rightarrow\:x\:=\:128}}}}$ ★

‎

Now let's substitute the value of x in the assumed value :

• Length = x = $\tt\purple{128\:m}$

• Breadth = x - 16 = 128 - 16 = $\tt\purple{112\:m}$

So now let's find the area of the rectangle :

$\sf\implies\:Area\:=\:length \times breadth$

• Substituting the values we got

$\sf\implies\:Area\:=\:128 \times 112$

$\small{\underline{\boxed{\mathrm\red{\rightarrow\:Area\:=\:14336\:sq.m}}}}$ ★

____________________‎

$\large\sf\underline{Verifying\::}$

Not sure about the answers we got let's verify it !

In order to verify we will substitute the value we have got in the equation which we had framed earlier. Solving that equation if we get LHS = RHS then our answers would be correct.

$\sf\to\:2(l+b) =480$

• Substituting the value of l and b

$\sf\to\:2(128+112) =480$

$\sf\to\:2(240) =480$

$\sf\to\:480 =480$

$\bf\to\:LHS =RHS$

$\large{\mathfrak\blue{hence\:verified\:!!}}$

____________________‎

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$\dag\:\underline{\sf So\:the\:area\:of\:the\:rectangle\:is\:14336\:sq.m}$

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!! Hope it helps !!

Answer 2

Answer:

$\fbox\purple{Diagram}$

$\begin{gathered}\begin{gathered} \blue{x \: m} \: \: \: \: \: \: \: \: \: \: \: \\ \pink{\boxed{\begin{array}{}\bf { \red{}}\\{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:}{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}}} \blue{ \tt \:(x-16) \: m} \end{gathered}\end{gathered}$

$\fbox\purple{Question}$

The breadth of the rectangle is 16m less than its length .The perimeter of the rectangle is 480m. Find the area of the rectangle.

$\fbox\purple{Given}$

Let the length of the rectangle be x

Breadth = (x - 16)

Perimeter = 480 m

$\fbox\purple{To\:find}$

Here we have to find Area of rectangle. But in the question we don't know the length and breadth so first we will find l and b then area.

$\fbox\purple{Formula}$

Perimeter of rectangle = 2(length + breadth)

Area of rectangle = length × breadth

$\fbox\purple{Solution}$

First we will find the length and breadth

Perimeter of rectangle = 2(length + breadth)

= 480 = 2{ x + ( x - 16)}

= 480 = 2{ x + x - 16}

= 480 = 2{ 2x - 16}

= 480 = 4x - 32

= 480 + 32 = 4x

= 512 = 4x

= 4x = 512

= x $\implies\sf \cancel\dfrac{512}{4}$

= x = 128

•°• x = 128 m

Lenght = x = 128 m

Breadth = ( x - 16) = 128 - 16 = 112

Now we need to find the area

Area of rectangle = length × breadth

= 128 × 112 = 14,336 m²

† The Area is 14,336 m²