Question

6 cm

M
x cm
O
4 cm
x cm
B
G
The area of rectangle ABCD is 28 cm²
a) What is the length of side AB in terms of x?
length of AB =
b) If the area of rectangle ABCD is 28 cm²,
we can show that x² + ax=b where
a and b are integer values.
Work out the values of a and b.
a=
46%
(1) b=
Total marks: 3

Answer 1

Explanation:

The length of AB is (x + 4) cm and the values of a and be are a = 10, b = 4

A rectangle is a quadrilateral in which opposite sides are equal and parallel to each other. The area of a rectangle is:

Area = length * width

From the image:

Length of AB = x + 4

Length of BC = x + 6

The area of rectangle ABCD = Length of AB * Length of BC

28 = (x + 4)(x + 6)

x² + 10x + 24 = 28

x² + 10x = 4

Comparing with x² + ax = b gives:

a = 10, b = 4

Therefore the length of AB is (x + 4) cm and the values of a and be are a = 10, b = 4