[CV062] A Tricky Inheritance

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061 - Pin Board Shapes

062 - A Tricky Inheritance

063 - Mother's Age

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A Tricky Inheritance
Game	Professor Layton and the Curious Village
Number	062
Type	Write Answer
Location	Manor Parlor
Solved by	Professor Layton
Picarats	40
Mandatory	No
Reward	Painting Scrap
In other languages
Deutsch	Erbendreieck
Español	Herencia peliaguda
Français	Legs peu commun
Italiano	L’eredità geometrica
한국의	유산의 삼각형 (Triangle of Heritage)

A Tricky Inheritance is a puzzle in the European version of Professor Layton and the Curious Village. For the puzzle in the American version of the game, go here.

Puzzle

A man made a rather unusual stipulation in his will regarding which of his three sons would inherit his estate.

"To the one who can work out the area of this triangular section of my estate, I bestow the entire inheritance."

Now the man has passed away and his sons are at a loss! Finding the area of his perfectly square estate is easy, but no one can find the area of the triangle.

Can you find the answer?

Hints

• →
• Hint 1
• Hint 2
• Hint 3

Click a Tab to reveal the Hint.

Let's review the method for finding the area of a right-angled triangle. You simply multiply the lengths of the two sides that make the right angle, and divide by 2.
You can use this method to solve the puzzle.

The only lengths you know for the square-shaped estate are 10m and 20m, so it should be easy to work things out. From the corner to the 10m point is half th length of a side of the square.
By drawing extra lines from these points, you can easily find the answer.

It's difficult to work out the area of the triangle directly, but it's a lot easier to find the areas of the three smaller triangles surrounding it.
If you find those areas and subtract them from the area of the square, you'll have the area of the large triangle.
Although there is an even better way...

Solution

Incorrect

Too bad!

Correct

That's right! It's 150 square metres.

There are several different ways to find the answer, but here's an interesting one. By drawing two lines on the diagram as shown in Figure 1, you can see that a and b are the same. By moving it from a to b as shown in Figure 2, you can make two right-angled triangles.

The rest is easy!