Question

The area of the rectangle ABCD is 28
`cm^(2)`

a) What is the length of side AB in terms of x?

length of AB = (Answer here) (1)

b) If the area of rectangle ABCD is 28
`cm^(2)`, we can show that
`x^(2)` + ax = b where a and b are integer values.

Work out the values of a and b.

a = (Answer here) (1) b = (Answer here) (1)

Answer 1

see explanation

Explanation:

(a)

AB = 4 + x

(b)

the area (A) of rectangle ABCD is calculated as

A = length × breadth

= AB × AD

= (4 + x)(6 + x) ← expand using FOIL

= 24 + 10x + x²

given A = 28 , then

x² + 10x + 24 = 28 ( subtract 24 from both sides )

x² + 10x = 4 ← in the form x² + ax = b

with a = 10 and b = 4