Question

Find Area when the rectangle's perimeter is 46cm and Diagonal is 17 cm .

Answer 1

$❤️Solution❤️$

Given

• Length of diagonal = 17cm
• Perimeter of Rectangle = 46cm

To Find

• Area of Rectangle

____________________

Let,

• Length of Rectangle be x.
• Breadth of Rectangle be y.

$\sf {\implies Perimeter~ of~ Rectangle = 2(Length+Breadth)}$

$\sf {\implies 46 = 2(x + y)}$

$\sf {\implies (x + y) = \dfrac{46}{2} }$

$\sf {\implies (x + y) = 23~~~~~----(1) }$

We know that

$\sf{\looparrowright(Diagonal)²=(Length)²+(Breadth)²}$

$\sf{\looparrowright(17)²=(x)²+(y)²}$

$\sf{\looparrowright x²+y² = 289 \: \: \: \: \: - - - - (2)}$

• Squaring Both Sides in Eq. (1)

$\sf {\implies (x + y)² = 23² }$

$\sf {\implies x²+ y² + 2xy = 529 }$

• Putting the Value x²+y²=289

$\sf {\implies 289 + 2xy = 529 }$

$\sf {\implies 2xy = 529 - 289 }$

$\sf {\implies 2xy = 240 }$

$\sf {\implies xy = 120 }$

$\sf {\implies Area~ Of~ Rectangle= Length× Breadth }$

$\sf {\implies Area~ Of~ Rectangle= xy }$

$\underline{\boxed{\bf\pink{ {\implies Area~ Of~ Rectangle= 120 {cm}^{2} } }}}$

Diagram

$\footnotesize\begin{gathered}\\\begin{gathered}\begin{gathered}\begin{gathered}\tiny\begin{gathered} {\begin{gathered}\sf{}\huge\boxed{ \begin{array}{cc} \: \: \: {\tiny{\sf{Area = 120cm²}}} \: \: \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \end{array}} \\ \: \: \: \: \: \sf{} \end{gathered}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

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

Answer 2

$\huge\fcolorbox{black}{magenta}{ ★Aηѕωєя᭄✍︎}$

Let the length of rectangle be l

And the breadth of rectangle be b.

Then, Diagonal of rectangle

=l² +b² =17

And, Perimeter of rectangle

→2(l+b)=46

→(l+b)=23

→(l+b)²=529

→l²+b²+2lb=529

→2lb=529−289

→lb=120

Thus, Area of rectangle = 120cm²