Question

A rectangle has a length 10 more than its width. If the width is increased by 8 and the length by 4, the resulting rectangle has an area
of 135 square units.
Part A
•
Write an equation to model the above scenario. Use the model to find the length of the original rectangle?
Part B
What is the perimeter of the expanded rectangle?

Answer 1

Answer:

The perimeter is 48

Step-by-step explanation:

If the width is W

AT first , Length is 10 +w

According to the question,

$(w+8) (10+w+4) = 135\\(w+8) (w+14) = 135\\\\w^{2} + 14w + 8w + 112- 135 = 0\\\\ w^{2} + 22w - 23 = 0\\(w+23) (w-1) = 0\\\\w+ 23 = 0 w-1=0\\\\w= -13 or w = 1$

Expended width will be  w +8 = 1+8 = 9

Length is 10+w+4 = 15

So the perimeter is

= i2 x (9+15)

= 2x 24

= 48

Answer 2

The Solution to the problem of the rectangle is given below

For Part A:

• equation model: (14 + w) * (w +8) = 132
• Length = 15

For Part B

• Perimeter = 46

Meaning of Perimeter

The perimeter of any shape can be defined as the total sum of the sides of the shape.

Analysis

For Part A

equation model= (14 + w) * (w +8) = 135

14w + 112 + 8w + $w^{2}$ = 135

$w^{2}$ + 22w - 23 = 0

solving the quadratic equation

w = -23 or 1

Because we are dealing with a physical quantity we will make use of the value 1

lenght of original rectangle = 10 + 1 = 11

Part B

Perimeter= 2(length) * 2 (breadth) = 2(11 + 4) * 2 (1 + 8)

Perimeter = 48

In conclusion, The Solution to the problem of the rectangle is given above.

Learn more about Perimeter: https://brainly.com/question/19819849

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