Question

A rectangular rug has an area
of 7x²-8x-12 square units. What is the lenth of the rectangle if width is (x-2)​

Answer 1

$\bigstar$ Question:

• A rectangular rug has an area of 7x²-8x-12 square units. What is the lenth of the rectangle if width is (x-2) ?

$\bigstar$Given:

• Area of the rectangular rug = 7x²-8x-12 square units.
• Width of the rectangle = ( x - 2 ) units

$\bigstar$To find:

• The length of the rectangular rug.

$\bigstar$ Solution:

Area of a rectangle = Length × Breadth

Given Area of the rectangular rug = 7x²-8x-12 square units

Breadth (Width) = ( x - 2 ) units

So Length = ?

Let the length be y.

A/q (x - 2) (y) = 7x² - 8x - 12

$\implies$ y = ( 7x² - 8x - 12 )/(x - 2)

$\implies$ $\boxed{y\: = \:7x\: + \:6\:}$

$\bigstar$Answer:

$\therefore$ the answer is 7x + 6.

$\star$ Verification:

• Dividend = 7x² - 8x - 12
• Divisor = (x - 2)
• Quotient = 7x + 6
• Remainder = 0

$\because$ Dividend = Quotient × Divisor + Remainder

$\implies$ 7x² - 8x - 12 = (7x + 6) × (x - 2) + 0

$\implies$ 7x² - 8x - 12 = 7x² - 14x + 6x - 12

$\implies$ LHS = RHS

Hence verified too.