Respuesta :
Answer:
a) the area of a square is in terms of x is
[tex](x+1)^2[/tex] 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 [tex]l^{2} = (x+1)(x+1)[/tex]
                 = [tex](x+1)^2[/tex]
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 Â = Â (x+1)(x+1 -5 )
now simplification [tex]24 = (x+1)^2 - 5 (x+1)[/tex]
apply (a+b)^2 = a^2+2 a b+b^2
[tex]x^2+2 x+1-5 x-5 =24[/tex]
[tex]x^2 -3 x -4-24=0[/tex]
[tex]x^{2} -3 x -28 =0[/tex]
now find factors of 28 Â = 7 X 4 is Â
[tex]x^{2} -7 x+4 x-28=0[/tex]
[tex]x(x-7)+4(x-7)=0[/tex]
[tex](x+4)(x-7)=0[/tex]
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
