The perimeter and area of a rectangle are 92 cm and respectively.
Find the length and the breadth of the rectangle.
peri -92 cm

Ask by Reeves Vaughan. in Singapore

Mar 26,2025

Question

The perimeter and area of a rectangle are 92 cm and $$ 480 \mathrm{~cm}^{2} $$ respectively. Find the length and the breadth of the rectangle. peri -92 cm

UpStudy AI · Accepted Answer

Given:
Perimeter of the rectangle = 92 cm
Area of the rectangle = 480 cm²

Let's denote the length of the rectangle as $$ l $$ and the breadth as $$ b $$.

The formula for the perimeter of a rectangle is:
$$ 2(l + b) = 92 $$

The formula for the area of a rectangle is:
$$ l \times b = 480 $$

We can solve these two equations simultaneously to find the values of $$ l $$ and $$ b $$.

Let's solve the equations.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}2\left(l+b\right)=92\lb=480\end{array}\right.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}b=46-l\lb=480\end{array}\right.$$
- step2: Substitute the value of $$b:$$
  $$l\left(46-l\right)=480$$
- step3: Expand the expression:
  $$46l-l^{2}=480$$
- step4: Move the expression to the left side:
  $$46l-l^{2}-480=0$$
- step5: Factor the expression:
  $$\left(-l+30\right)\left(l-16\right)=0$$
- step6: Separate into possible cases:
  $$\begin{align}&-l+30=0\&l-16=0\end{align}$$
- step7: Solve the equation:
  $$\begin{align}&l=30\&l=16\end{align}$$
- step8: Calculate:
  $$l=30\cup l=16$$
- step9: Rearrange the terms:
  $$\left\{ \begin{array}{l}b=46-l\l=30\end{array}\right.\cup \left\{ \begin{array}{l}b=46-l\l=16\end{array}\right.$$
- step10: Calculate:
  $$\left\{ \begin{array}{l}b=16\l=30\end{array}\right.\cup \left\{ \begin{array}{l}b=30\l=16\end{array}\right.$$
- step11: Check the solution:
  $$\left\{ \begin{array}{l}b=16\l=30\end{array}\right.\cup \left\{ \begin{array}{l}b=30\l=16\end{array}\right.$$
- step12: Rewrite:
  $$\left(b,l\right) = \left(16,30\right)\cup \left(b,l\right) = \left(30,16\right)$$
The solutions to the system of equations are:
$$ (b, l) = (16, 30) $$ or $$ (b, l) = (30, 16) $$

Therefore, the length and breadth of the rectangle are either 16 cm and 30 cm or 30 cm and 16 cm.
The length and breadth of the rectangle are 16 cm and 30 cm, or 30 cm and 16 cm.

The perimeter and area of a rectangle are 92 cm and respectively.
Find the length and the breadth of the rectangle.
peri -92 cm

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The perimeter and area of a rectangle are 92 cm and respectively. Find the length and the breadth of the rectangle. peri -92 cm