The length of a rectangle is (x + 1) cm and its width is 5cm less than its length.

a) express a square, l cm, in x.

b) given a rectangle is 24cm, calculate the length and width of the square

a) the area of a square is in terms of x is

centimeter square

b)The length of the rectangle is l = (x+1)

                                       l = 7+1 =8 cm

The width of the rectangle is w = [(x+1)-5]

                                     w = (7+1)-5 =3 cm

Step-by-step explanation:

a) the area of a square is in terms of x is

 area of square is

                                 =

b)  Given length is  l = (x+1) cm and

the width is 5 cm less than its length.

so we have take width is w = (x+1)-5 cm

Given area of triangle is  24 cm

Area of rectangle = length X width

24  =  (x+1)(x+1 -5 )

now simplification

apply (a+b)^2 = a^2+2 a b+b^2

now find factors of 28  = 7 X 4 is  

x = -4 and x=7

there fore you have to choose x = 7

The length of the rectangle is l = (x+1)

                                       l = 7+1 =8

The width of the rectangle is w = [(x+1)-5]

                                     w = (7+1)-5 = 3

Verification:-

Given area of rectangle  = 24 = 8 X 3

                                           24 =24

so we can not choose x=-4

we have to choose x =7 only

step-by-step explanation:

in which figure is point g a centroid

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15