a rectangle has a length that is 2 less than 3 times the width of the area of rectangle is 16 find the dimensions and perimeter
Answers (2)
25th Jun, 2020
Help there,
Let's solve the problem:
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.
Answer:
L= 6 unit.
B= 2.6 unit.
Perimeter= 17.2 unit.
Hope this answer helps you.
Thank you!!
Let's solve the problem:
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.
Answer:
L= 6 unit.
B= 2.6 unit.
Perimeter= 17.2 unit.
Hope this answer helps you.
Thank you!!
Comments (0)
25th Jun, 2020
Hello!
Let the width(b) of the rectangle be 'x'.
Length, l = 3x - 2
Area of the rect. = l × b
16 = (3x - 2)*x
16 = 3x^2 - 2x
the equation is 3x^2 - 2x - 16 = 0
Now we will factorise this equation:-
3x^2 - 2x - 16
3x^2 - 8x + 6x - 16
3x^2 + 6x - 8x - 16
3x(x + 2) -8(x + 2)
(3x - 8)(x + 2)
Hence possible values of x can be 8/3 or -2.
Since the breadth can't be negative,
x = 8/3
Now, 3x - 2 = 3*(8/3) - 2
= 8 - 2 = 6 cm
Now, perimeter, P = 2(l + b)
P = 2(6 + 8/3)
P = 2(18 + 8/3)
P = 26/3 × 2
P = 52/3 cm
Hence the perimeter of the rectangle is 52/3 cm.
Thankyou!
Hope it helps!
Comments (0)
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