ESAT Mock Maths 1 Esat-maths1-challenge-3

1 questions1 marks40Updated August 2026

The ESAT Mock Maths 1 Esat-maths1-challenge-3 paper in full: all 1 questions, each with its answer. ESAT is the Engineering and Science Admissions Test. Sit it cold under exam timing, mark it, then work back through anything you missed using the solutions below.

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Question 1

1 mark

A rectangle has a perimeter of

28\,\text{cm}

and a diagonal of length

10\,\text{cm}

. A student is asked to find the area of the rectangle, and argues as follows: since there are two unknowns (the side lengths) and only two pieces of information, there must be a unique rectangle, so the area can be found. Which of the following is the correct conclusion?

A.The area is uniquely determined and equals $48\,\text{cm}^2$
B.There are two possible rectangles with different areas, $24\,\text{cm}^2$ and $48\,\text{cm}^2$
C.The area is uniquely determined and equals $24\,\text{cm}^2$
D.No such rectangle exists
E.There are two possible rectangles, but they have the same area, $48\,\text{cm}^2$
F.There are two possible rectangles, but they have the same area, $24\,\text{cm}^2$

Answer: F

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