Question

Aere are two squares. A and B.

A
B
The length of each side of square B is 4 cm greater than the length of each side of square A.
The area of square B is 70 cm² greater than the area of square A.
Find the area of square B.
Give your answer correct to 3 significant figures.
You must show all your working.

Answer 1

116 cm²

Explanation:

a = side length of A

b = side length of B

b = a + 4

b² = a² + 70

(a+4)² = a² + 70

a² + 8a + 16 = a² + 70

8a + 16 = 70

8a = 54

a = 54/8 = 27/4 = 6.75

b² = a² + 70 = 6.75² + 70 = 45.5625 + 70 =

= 115.5625 ≈ 116 cm²

our does your teacher mean 3 significant figures after the decimal point ? then it would be

115.563 cm²

Answer 2

The area of square B is 115.563 cm²

Defining our parameters as follows ;

• side length A = a
• side length of B = b

Area of a square = (side length)²

b = 4 + a ___(1)

b² = 70 + a² __(2)

substitute (1) into (2)

(a + 4)² = 70 + a²

a² + 8a + 16 = 70 + a²

a² - a² + 8a = 70 - 16

8a = 54

a = 54/8

a = 6.75

The side length of square B is ;

• a + 4 = 6.75 + 4 = 10.75 cm

The area of square B is ;

Area = 10.75²

Area = 115.563 cm²