Question

Q2. The length and breadth of a rectangle are (2x + 3) cm and x+4) cm respectively. If the area of the rectangle is 88 cm2 find

(a) the value of x,
(b) the perimeter of the rectangle.​

Answer 1

Answer:

(a) Value of x = 4
(b) Perimeter of the rectangle = 38cm

Step-by-step explanation:

Length of the rectangle = (2x + 3) cm
Breath of the rectangle = (x + 4) cm
Area of the rectangle = length x breadth
Area  given = 88 square cm

So, (2x + 3) x (x + 4) = 88 sq cm
2x (x + 4) + 3 (x + 4) -- this is multiplication of binomials
2x² + 8x + 3x + 12 = 2x² + 11x + 12
2x² + 11x + 12 = 88
2x² + 11x = 88 - 12 (transposition method)
2x² + 11x = 76
And after this I did trial and error method, by substituting values of x from 1 because I don't know how to do other than this way.
x = 4 satisfies the equation
2 X (4²) + (11 X 4) = (2 x 16) + 44 = 32 + 44 = 76
So x = 4,
Perimeter of a rectangle = 2 (length + breath)
Length = (2x + 3) = {(2 X 4) + 3} = 8 + 3 = 11
Breadth = (x + 4) = 4 + 4 = 8
Perimeter = 2 X (11 + 8) = 2 X 19 = 38cm

Hope this helped you!