Question

PLEASE HELP ME!!!

The area of a rectangle is given by the expression 4x^2 + 5x − 6.
a) What is the length of the rectangle if the width is x + 2?
b) If x = 11 cm, find the length, width, and area.
The area of the square rug is 121x^2 − 22x + 1.
a) Find the dimension of the rug in terms of x.
b) If x = 25 cm, find the side length and the area of the rug. 29-30. A square painting is surrounded by a 12-centimeter wide frame. If the total area of the painting plus frame is 1225 cm^2, find the dimension of the painting and the x values.

Answer 1

Explanation:

a)

put the formula....

l × b = A

or,

`l × ( x+2 ) = 4{x}^(2) + 5x - 6`

or,

`l *(x + 2) = (4x - 3)(x + 2)`

or,

`l = (4x - 3) + (x + 2) - (x + 2)`

Therefore,

`l = 4x - 3`

b)

we know the value of x,

l = 4x-3 b = x+2

= 4× 11 -3 = 11+2

= 41cm = 13cm

Area= l × b

= 41 × 13

= 533 cm^2

c)

square = l × l

Given,

121x^2 - 22x + 1

or, 121x^2 -11x -11x +1

or, 11x ( 11x -1 ) - 1 ( 11x -1 )

Therefore,

dimension is ( 11x-1 )( 11x -1 )

d) x= 25

l= 11x -1

= 11× 25 -1

= 274cm

Area= l^2

= 75076 cm^2

Area of frame = (12cm)^2

= 144cm^2

Area of painting= ( 1225-144 )cm^2

= 1081 cm^2

(length)^2 = Area

or, l^2 = (1081)

or 1^2 = (32.8)^2

Therefore, dimension of painting is 32.8cm