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Question id: 124. This question is similar to one that appeared in a GCSE Higher paper (specimen) for 2017. The use of a calculator is allowed.

### Mensuration

A square has sides of length $$x$$ cm.

The equilateral triangle next to it has sides which are each 3cm more than the length of a side of the square.

(a) Find the perimeter of the square if it is equal to the perimeter of the triangle.

The diagram above show the same square and triangle.

The length of the diagonal of the square is $$d$$ cm and the height of the triangle is $$h$$ cm.

(b) Which has the greater value, $$d$$ or $$h$$?

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