Question

A rectangle has a width that is 7 centimeters less than its length, and its area is 330 square centimeters. What are the dimensions of the rectangle?

Answer 1

Let length of rectangle be x cm.

A rectangle has a width that is 7 centimeters less than its length.

Width = (x - 7) cm

Area of rectangle = 330 cm²

Area of rectangle = length × breadth

Substitute the known values in above formula

=> 330 = x(x - 7)

=> 330 = x² - 7x

=> x² - 7x - 330 = 0

=> x² - 22x + 15x - 330 = 0

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

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

=> x = 22, -15

[-15 neglected as length can't be negative]

So,

Length of rectangle = 22 cm

Breadth of rectangle = 22 - 7

=> 15 cm

•°• Dimensions of the rectangle are 22 and 15 cm respectively.

Answer 2

$\bold{\underline{\underline{Answer:}}}$

Length = 22 cm

Breadth (width) = 15 cm

$\bold{\underline{\underline{Step\:by\:step\:explanation:}}}$

Given :

• A rectangle has a width that is 7 centimeters less than its length
• Area of rectangle = 330 sq. cm

To find :

• Dimensions of the rectangle

1. Length
2. Breadth (width)

Solution :

Let the length of the rectangle be x cm.

$\bold{\underline{\underline{As\:per\:the\:given\:condition:}}}$

• Width is 7 centimeters less than its length

•°• Width of rectangle = (x - 7) cm

We have the area of the rectangle. So using the formula for area of a rectangle we can solve the question further.

$\bold{\large{\boxed{\blue{\rm{Area\:of\:a\:rectangle\:=\:Length\:\times\:width}}}}}$

Block in the values,

$\rightarrow$ $\bold{330=(x)(x-7)}$

$\rightarrow$ $\bold{330=x^2-7x}$

$\rightarrow$ $\bold{x^2-7x=330}$

$\rightarrow$ $\bold{x^2-7x-330=0}$

Solve the quadratic equation so formed by factorization method,

$\rightarrow$$\bold{x^2-22x+15x-330=0}$

$\rightarrow$$\bold{x(x-22) + 15(x - 22)=0}$

$\rightarrow$$\bold{(x-22) (x+15)=0}$

$\rightarrow$$\bold{(x-22)=0\:\:\:OR\:\:\:(x+15)=0}$

$\rightarrow$$\bold{x-22=0\:\:\:OR\:\:\:x+15=0}$

$\rightarrow$$\bold{x=22\:\:\:OR\:\:\:x=-15}$

x = - 15 is neglected since length cannot be negative.

•°• Length = x = 22 cm

Breadth = x - 7 = 22 - 7 = 15 cm

Dimensions :-

1. Length = 22 cm
2. Breadth (width) = 15 cm