Question

the length of a rectangle is greater than 4 times its breadth by 5cm. if it's length is reduced by 2cm and breadth is increased by 2cm,then the area of the rectangle increased by 36cm2. find the length and breadth of the original rectangle​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

• Breadth of rectangle = 'x' cm

So,

• Length of the rectangle = 4x + 5 cm

We know,

$\rm :\longmapsto\:Area_{(rectangle)} = Length \times Breadth$

$\rm :\longmapsto\:Area_{(rectangle)} = x \times (4x + 5)$

$\bf :\longmapsto\:Area_{(rectangle)} = 4 {x}^{2} + 5x - - - (1)$

Again,

Given that,

☆ If length is reduced by 2 cm and breadth isincreased by 2 cm, then the area of the rectangle increased by 36 cm^2.

So,

• Length of rectangle = 4x + 5 - 2 = 4x + 3 cm

• Breadth of rectangle = x + 2

$\rm :\longmapsto\:Area_{(rectangle)} = (4x + 3)(x + 2)$

$\rm :\longmapsto\:Area_{(rectangle)} = 4 {x}^{2} + 3x + 8x + 6$

$\rm :\longmapsto\:Area_{(rectangle)} = 4 {x}^{2} + 11x + 6 - - - (2)$

☆ According to statement,

$\rm :\longmapsto\: {4x}^{2} + 11x + 6 = {4x}^{2} + 5x + 36$

$\rm :\longmapsto\:6x = 30$

$\bf\implies \:x = 5 \: cm$

Hence,

• Breadth of rectangle = 5 cm

• Length of rectangle = 4x + 5 = 4 × 5 + 5 = 25 cm

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.