Question

A rectangle is shown below.
All measurements are to the nearest cm
Measurements 17cm lengthways
9cm downwards
A) calculate the lower bond of the rectangle area
B) calculate the upper bond of the rectangle perimeter

Answer 1

Given:

The dimensions of the rectangle:

Length = 17 cm

Breadth = 9 cm

To find:

A) calculate the lower bond of the rectangle area

B) calculate the upper bond of the rectangle perimeter

Solution:

Since the measurements of the length and breadth of the rectangle are given to its nearest cm

i.e., The degree of accuracy of the measurements is to the nearest 1 cm

So, 1 cm ÷ 2 = 0.5 cm

For length of the rectangle:

Upper bound = 17 + 0.5 = 17.5 cm

Lower bound = 17 - 0.5 = 16.5 cm

For breadth of the rectangle:

Upper bound = 9 + 0.5 = 9.5 cm

Lower bound = 9 - 0.5 = 8.5 cm

Now,

(A). Finding the lower bound of the rectangle area:

Minimum Area of the rectangle is given by,

= [length(lower bound)] × [breadth(lower bound)]

= 16.5 × 8.5

= 140.25 cm²

Thus, the lower bond of the rectangle area is 140 cm².

and

(B). Finding the upper bound of the rectangle perimeter:

Maximum perimeter of the rectangle is given by,

= 2 [length(upper bound) + breadth(upper bound)]

= 2[17.5 + 9.5]

= 54 cm

Thus, the upper bound of the rectangle perimeter is 54 cm.

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