## Brain-Teaser 471

**From The Sunday Times, 7th June 1970** [link]

Plott was showing Green his garden. “A fine lawn”, commented Green. “Thank you. It’s remarkable, too. The sides run exactly north-south and east-west.”

The strolled to a flower bed cut in the lawn. “When I came here”, said Plott, “there was just a triangle. One side, of 15 feet, was parallel to the north side of the lawn, and from its western end the second side rand due south for 22 feet. Rather a miserable affair. So I constructed these squares outwards from two sides; the north edge of the small square ran exactly along the north side of the lawn, while one corner of the large square just touched the east side of the lawn — where the flagpole now stands. But I want to enlarge it again”.

“If I might make a suggestion”, replied Green, “you could join up the outside corners of the squares and give the bed a nice five-sided outline”. Plott thought this a good idea.

Next day he ran a line from the flagpole to the north-east corner of the small square, and then worked on the triangle formed by this line, to east side of the small square and the side of the large square running from the small square to the flagpole.

How many square feet were in this new piece?

[teaser471]

## Jim Randell 12:48 pm

on13 April 2019 Permalink |This is mostly an exercise in following the instructions to draw the following diagram:

Red line segments are 15 ft, green line segments 22 ft, and blue line segments √(709) ft (but we don’t need to know that).

We start with the right-angled triangle with red, green, blue sides on the left, and then add the red and blue squares. This lets us construct the desired (yellow shaded) triangle, which we see has a red N-S “base” of 15 ft, and by placing a second red, green, blue triangle within the blue square, we see the desired triangle has a green W-E “height” of 22ft. So it has the same area as the original triangle.

Solution:The area of the triangle is 165 sq. ft.LikeLike