Question

A rectangle had a width that is 7 centimeters less then its length, and it’s area is 330 square centimeters

Answer 1

The length of rectangle is 22cm and width is 15cm.

Explanation:

Let x is length of rectangle.

let x-7 is the width of rectangle.

Area is given .

A = 330 cm²

The formula for area of rectangle is

A = length × width

Putting above values in above equation, we have

330 = x(x-7)

330 = x²-7x

x²-7x-330 = 0

We solve above equation by factoring.

Split the middle term of above equation, we have

x²-22x+15x-330 = 0

Making two groups, we have

x(x-22)+15(x-22) = 0

Taking x-22 as common, we have

(x-22)(x+15) = 0

Applying Zero Product Propert, we have

x-22 = 0 or x+15= 0

x=22 or x=-15

Length of rectangle can not be negative.

Hence, x = 22 is true.

x-7 = 22-7=15

Then, the length of rectangle is 22cm and width is 15cm.

Answer 2

Answer: Dimensions of rectangle are 22 cm and 15 cm respectively.

Explanation:

Since we have given that

Let the length of rectangle be x

Let the width of rectangle be x-7

As we know the formula for "Area of rectangle":

`Area=length* breadth\\\\330=x* (x-7)\\\\330=x^2-7x\\\\x^2-7x-330=0\\\\x^2-22x+15x-330=0\\\\x(x-22)+15(x-22)=0\\\\(x-22)(x+15)=0\\\\x=22,-15\\\\\text{But dimension can't be in negative}\\\\x=22\ cm`

Hence, Length of rectangle = 22 cm

Width of rectangle = 22-7 = 15 cm.