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Maths

Loci

Problems involving loci

Question

Two goats graze in a field of length 20m and width 12m. They are tethered to diagonally opposite corners by ropes of length 13m. On a scale drawing, show the area grazed by both goats.

goat

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Answer

Did you remember to use your compass? If so - well done!

If you did not get this right, here are some tips:

The question asks for a scale drawing. An appropriate scale would be 2m = 1cm. So on your drawing:

20m = 10cm

12m = 6cm

13m = 6.5cm

Do not forget to write the scale next to the diagram.

Next, measure a distance of 6.5cm using your compass. Place your compass point on one corner of the rectangle, and draw an arc. Do the same for the diagonally opposite corner.

The area between these 2 arcs is the area grazed by both goats.

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