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Mensuration: Areas and Volumes · Question 5 of 68

Question 5

EasyOriginal question

A rectangular hall floor measures 32 m by 18 m. A square courtyard has exactly the same area. By how much does the perimeter of the hall floor exceed the perimeter of the courtyard?

Options for question 5

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. Area of the hall = 32×18=57632 \times 18 = 576 m², so the courtyard's side = 576=24\sqrt{576} = 24 m.

  2. Perimeters: hall 2×(32+18)=1002 \times (32 + 18) = 100 m, courtyard 4×24=964 \times 24 = 96 m.

  3. Difference = 100−96=4100 - 96 = 4 m.

Worth noting

Equal areas do not mean equal perimeters, so 0 m is wrong. For a fixed area, the square has the smallest perimeter of all rectangles.

Concept
Equal areas, different perimeters
Typical time
40 s
Your time
—
The rule this testsPerimeter and area
Practise this chapter →

Ten questions from Mensuration: Areas and Volumes, at your own pace.

Practise this chapter →

Ten questions from Mensuration: Areas and Volumes, at your own pace.