Question

I need help with these maths questions

Answer 1

a) Because two opposite sides of the rectangle have the same sizes

B)

`x = (11)/(2)`

c)

`57`

Explanation:

b)

`4x + 1 = 2x + 12 \\ 4x - 2x = 12 - 1 \\ 2x = 11 \\ (2x)/(2) = (11)/(2) \\ x = (11)/(2)`

c) Perimeter

`p = 2(x + y) \\ 2( (11)/(2) + 23) \\ 2( (57)/(2) ) \\ 57`

23 comes from

`2x + 12 \\ x = (11)/(2) \\ 2( (11)/(2) ) + 12 \\ 11 + 12 \\ \\ 23`

Answer 2

see explanation

Explanation:

(a)

• the opposite sides of a rectangle are congruent

then

4x + 1 = 2x + 12

(b)

solving

4x + 1 = 2x + 12 ( subtract 2x from both sides )

2x + 1 = 12 ( subtract 1 from both sides )

2x = 11 ( divide both sides by 2 )

x = 5.5

(c)

the perimeter (P) is the sum of the 4 sides of the rectangle , that is

P = 4x + 1 + x + 2x + 12 + x ( collect like terms )

= 8x + 13 ( substitute x = 5.5 )

= 8(5.5) + 13

= 44 + 13

= 57