Question

A rectangle is 5 cm long and 3 cm wide. Its perimeter is doubled when each of its sides is increased by x cm. Find an equation in x and find its new length​

Answer 1

The answer is given above...

Hope it helps...

Plz mark as brainliest...

Answer 2

$\huge\mathfrak\blue{ANSWER}$

Given :-

A rectangle is 5 cm long and 3 m wide(breadth).

Its perimeter is doubled when each of its sides is increased by x cm.

To Find :-

What is the new length of rectangle.

Formula Used :-

$\clubsuit♣ Perimeter \: of \: a \: Rectangle \: Formula :$

$=\: 2(Length + Breadth)$

⟼

Perimeter

(Rectangle)

=2(Length+Breadth)

Solution :-

First, we have to find the original perimeter of rectangle :

$\implies \sf Original\: Perimeter_{(Rectangle)} =\: 2(5 + 3)⟹OriginalPerimeter$

(Rectangle)

=2(5+3)

$\implies \sf Original\: Perimeter_{(Rectangle)} =\: 10 + 6⟹OriginalPerimeter </p><p>(Rectangle)$

=10+6

$\implies \sf \bold{\green{Original\: Perimeter_{(Rectangle)} =\: 16\: cm}}⟹OriginalPerimeter </p><p>(Rectangle)$

=16cm

Let,

$\mapsto↦ New length = (5 + x) cm$

$\mapsto↦ New breadth = (3 + x) cm$

According to the question by using the formula we get,

$\implies \sf 2\{(5 + x) + (3 + x)\} =\: 2 \times 16⟹2{(5+x)+(3+x)}=2×16$

$\implies \sf 2(5 + x + 3 + x) =\: 32⟹2(5+x+3+x)=32$

$\implies \sf 10 + 2x + 6 + 2x =\: 32⟹10+2x+6+2x=32$

$\implies \sf 10 + 6 + 2x + 2x =\: 32⟹10+6+2x+2x=32$

$\implies \sf 16 + 4x =\: 32⟹16+4x=32$

$\implies \sf 4x =\: 32 - 16⟹4x=32−16$

$\implies \sf 4x =\: 16⟹4x=16$

$\implies \sf x =\: \dfrac{\cancel{16}}{\cancel{4}}⟹x= </p><p>4$

16

$\implies \sf x =\: \dfrac{4}{1}⟹x= </p><p>1</p><p>4$

$\implies \sf\bold{\purple{x =\: 4\: cm}}⟹x=4cm$

Hence, the required new length and breadth are :

$\mapsto↦ New \: length \: of \: Rectangle :$

$\longrightarrow \sf (5 + x)\: cm⟶(5+x)cm$

$\longrightarrow \sf (5 + 4)\: cm⟶(5+4)cm$

$\longrightarrow \sf\bold{\red{9\: cm}}⟶9cm$

$\mapsto↦ New \: breadth \: of \: Rectangle :$

$\longrightarrow \sf (3 + x)\: cm⟶(3+x)cm$

$\longrightarrow \sf (3 + 4)\: cm⟶(3+4)cm$

$\longrightarrow \sf\bold{\red{7\: cm}}⟶7cm$

$\therefore \: The \: new \: length \: of \: rectangle \: is \: 9 \: cm .$