Question

a rectangle has a length that is 2 less than 3 times the width if the are of rectangle is 16 find the dimensions and the perimeter

Answer 1

Let the width be x

Length = 3x-2 ( 2 less than 3 times the width )

Area = 16cm²

x ( 3x - 2 ) =16

• 3x² - 2x - 16 = 0
• 3x² - 6x + 8x - 16 = 0
• 3x ( x - 2) + 8 ( x- 2 ) = 0
• ( x - 2 ) ( 3x + 8 ) = 0

So x = 2.

Width = 2 cm

Length = 4 cm

hope it helps u dear .....

Answer 2

Answer:

Dimensions are

Length = 6 unit.

Breadth = 2.6 unit.

Perimeter = 17.2 unit.

Step-by-step explanation:

Let, L and B be the length and breadth of the rectangle, respectively.

Now, given that,

L= 3B - 2, and,

Area= L×B= 16 sq.unit

According to the given problem,

B(3B-2) = 16

or, 3B - 2B = 16

or, 3B - 2B - 16 = 0

or, 3B + 6B - 8B - 16 = 0

or, 3B (B+2) - 8 (B+2) = 0

or, (B+2) (3B-8) = 0

Now, B cannot be -2, since breadth cannot be negative.

Hence, B is 8/3, which is 2.6 unit.

L= 3B -2 = 6 unit.

Perimeter= 2 (L+B) = 17.2 unit.