Question

the length of rectangular shaped card board is 10 inches longer than its width what are the dimensions of the card board if it has an area of 375in

Answer 1

Answer :-

Given :-

• Length = Width + 10 inches
• Area = 375 sq. inches

To Find :-

• Dimensions of rectangular cardboard

Solution :-

Let the width be x.

Length = x + 10

We know that,

Area of rectangle = Length × Width

Substituting the value in formula :-

→ 375 = x ( x + 10 )

→ 375 = x² + 10x

→ x² + 10x - 375 = 0

Using the middle term splitting method :-

→ x² + 25x - 15x - 375 = 0

→ x ( x + 25 ) - 15 ( x + 25 ) = 0

→ ( x - 15 ) ( x + 25 ) = 0

→ x = 15 , -25

As negative dimension is not possible,

x = 15

• Width = x = 15
• Length = x + 10 = 25

Dimensions of cardboard are 15 inches and 25 inches

Answer 2

Let

• Width be x

Given

• Length= 10 + x
• Area = 375 inches²

To Find

• Length and width

Formula Used

• Area of Rectangle= Length×width

Solution

${\sf~~~~~:~~\implies375 = (10 + x)x}$

${\sf~~~~~:~~\implies 10x + {x}^{2} = 375 }$

${\sf~~~~~:~~\implies x²+10x - 375 = 0 }$

• By splitting middle

${\sf~~~~~:~~\implies x²+25x-15x - 375 = 0 }$

${\sf~~~~~:~~\implies x(x+25)-15(x + 25) = 0 }$

${\sf~~~~~:~~\implies (x+25)(x - 15)= 0 }$

${\sf~~~~~:~~\implies x = 15 \: \: \: \: \: \: \: \: \: \: \: x = - 25 }$

We know that

• Dimensions of Figure Never be in Negative

So,

• width of Rectangle= 15inches
• Length of Rectangle= 15+10=25 inches

_____________________

Diagram:

$\begin{gathered}\\\begin{gathered}\begin{gathered}\begin{gathered}\tiny\begin{gathered} {\begin{gathered}\sf{15 \:inches~~~}\huge\boxed{ \begin{array}{cc} \: \: \: {\tiny{\sf{Happy~Studying}}} \: \: \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \end{array}} \\ \: \: \: \: \: \sf{25 \: inches~~~} \end{gathered}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \bigstar \: \underline{\mathfrak{More \: Useful \: Formula}}\\ {\boxed{\begin{array}{cc}\dashrightarrow {\sf{Perimeter \: of \: rectangle = 2(l + b)}} \\ \\ \dashrightarrow \sf{Area \: of \: rectangle = length \: \times breadth }\\ \\ \dashrightarrow \sf{Perimeter \: of \: square = 4 \times side } \\ \\ \dashrightarrow \sf{Area \: of \: square =(side) ^{2} } \\ \\ \dashrightarrow \sf{Area \: of \: parallelogram = base \times height} \\ \\ \dashrightarrow \sf{Area \: of \: trapezium = \frac{1}{2}×sum \: of \: parallel \: side \: \times \: height }\\ \end{array}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$