12. The length and width of a rectangle are in the ratio 7:3. If the perimeter is 62cm calculate: (1) the width (ii) the length of a diagonal to the nearest centimetre. (iii) the area of the rectangle.​

Step-by-step explanation:

Length = 7x

Width = 3x

Perimeter = 2L + 2W

Part A

2*7x + 2*3x = 62

14x + 6x = 62

20x = 62

x = 62/20

x = 3.1

Length = 3.1 * 7     21.7

Width = 3.1 *3        9.3

Width = 9.3

Part B

Use the Pythagorean Theorem

diagonal squared = 21.7^2 + 9.3^2

diagonal^2 = 557.38

sqrt(diagonal^2) = sqrt(557.38)

diagonal = 23.61

To the nearest cm is 24

Part C

Area = L*W

Area = 21.7 * 9.3

Area = 201.8

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