Verified answer

Question:-

The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the original rectangle. Find the length and the breadth of the original rrectangle

Answer:

[tex]\begin{gathered}\qquad \:\boxed{\begin{aligned}& \qquad \:\bf \:Breadth_{(Rectangle)} \: =9 \: cm \qquad \: \\ \\& \qquad \:\bf \: Length_{(Rectangle)}=16 \: cm\end{aligned}} \qquad \\ \\ \end{gathered}[/tex]

Step-by-step explanation:

Given that, length of a rectangle exceeds its breadth by 7 cm.

Let assume that Breadth of a rectangle = x cm

So, Length of a rectangle = x + 7 cm

We know,

[tex]\begin{gathered}\sf \: Area_{(Rectangle)} = Length \times Breadth \\ \\ \end{gathered}[/tex]

So, on substituting the values, we get

[tex]\begin{gathered}\sf \: Area_{(Rectangle)} = x(x + 7) - - - (1) \\ \\ \end{gathered}[/tex]

Now, Further given that, the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the original rectangle.

So,

• Length of a rectangle = x + 7 - 4 = x + 3 cm

• Breadth of a rectangle = x + 3 cm

So,

[tex]\begin{gathered}\sf \: Area_{(Rectangle)} = (x + 3) \times (x + 3) \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: Area_{(Rectangle)} = {(x + 3)}^{2} - - - (2) \\ \\ \end{gathered}[/tex]

According to statement, area of rectangle in both the cases are same.

[tex]\begin{gathered}\sf \: x(x + 7) = {(x + 3)}^{2} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: {x}^{2} + 7x = {x}^{2} + {3}^{2} + 2(x)(3) \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: 7x = 9 + 6x \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: 7x - 6x= 9 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf\implies \sf \: x= 9 \\ \\ \end{gathered}[/tex]

Hence,

[tex]\begin{gathered}\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \:Breadth_{(Rectangle)} \: =9 \: cm \qquad \: \\ \\& \qquad \:\sf \: Length_{(Rectangle)}=16 \: cm\end{aligned}} \qquad \\ \\ \end{gathered}[/tex]

[tex]\rule{190pt}{2pt}[/tex]

Answer:

Breadth=9cm

length=16cm

Step-by-step explanation:

let the Breadth=X cm

The length exceed 7cm=(X+7)cm

Breadth is exceed by 3-(X+3)cm

length is decreased by

4=(X+7-4)=X+3 cm

Area-length-Breadth

According To The Question

X(X+7)=(X+3)x(X+3)

x^2+7x=x^2+3x+3x+9

x^2+7x-x^2-3x-3x-9=0

7x-6x=9

X=9

Breadth=9cm

Length=9+7=16cm