the width of a rectangle is 4cm and the length is 8 cm if both the width and the length are increased by equal measures, the area of the rectangle is increased by 64 cm 2. find the length and width of the larger rectangle

(4+x)(8+x) = 4*8 + 64

x^2+12x-64 = 0
(x-4)(x+16) = 0

x = 4
So, the rectangle is
8x12 with area 96 (32+64)

a rectangle of length 12cm and breadth 9cm has its length increase by 4cm what is the increase in its area

A rectangle of length 12cm and breadth 9cm has its length increased by 4cm. What is the increase in its area

To find the length and width of the larger rectangle, we need to determine the measure by which both the width and the length are increased.

Let's denote the increase in measure by 'x'.

According to the given information, the original width is 4 cm and the original length is 8 cm. When both dimensions are increased by 'x' cm, the new width becomes (4 + x) cm and the new length becomes (8 + x) cm.

The area of a rectangle is calculated by multiplying its length and width. So, the original area of the rectangle is 4 cm * 8 cm = 32 cm^2.

The area of the larger rectangle is obtained by increasing the original area by 64 cm^2. Therefore, the area of the larger rectangle is 32 cm^2 + 64 cm^2 = 96 cm^2.

We can use this information to set up an equation:

(4 + x) cm * (8 + x) cm = 96 cm^2

Simplifying this equation:
32 + 12x + x^2 = 96

Rearranging the equation to solve for 'x':
x^2 + 12x - 64 = 0

Factoring or using the quadratic formula, we find:
(x + 16)(x - 4) = 0

This equation has two solutions: x = -16 and x = 4. However, since 'x' represents an increase in measure, we discard the negative solution. Therefore, x = 4.

Substituting x = 4 back into the original equations for width and length, we can find the dimensions of the larger rectangle:

Width = Original Width + Increase in Measure = 4 cm + 4 cm = 8 cm

Length = Original Length + Increase in Measure = 8 cm + 4 cm = 12 cm

Therefore, the length and width of the larger rectangle are 12 cm and 8 cm, respectively.