Let’s solve this step by step.
We are told:
- All triangles have a right angle.
- The yellow triangle is also an
isosceles triangle (meaning two sides are equal).
- We need to find the length of the sides of the
yellow triangle.
Looking at the diagram, the yellow triangle sits on top of a blue triangle that has one side labeled “4cm”. That 4cm side is shared with the yellow triangle — so one side of the yellow triangle is 4cm.
But wait — we’re told the yellow triangle is
isosceles, and it’s a right-angled triangle. In a right-angled isosceles triangle, the two legs (the sides forming the right angle) are equal. So if one leg is 4cm, the other leg must also be 4cm.
Then, the hypotenuse (the longest side, opposite the right angle) can be found using Pythagoras’ theorem:
> a² + b² = c²
> where a and b are the legs, and c is the hypotenuse.
So for the yellow triangle:
- a = 4 cm
- b = 4 cm
- c = ?
c² = 4² + 4² = 16 + 16 = 32
→ c = √32 = √(16 × 2) = 4√2 ≈ 5.66 cm
But let’s double-check: Is the 4cm side really a leg of the yellow triangle?
Looking again at the diagram: The blue triangle below the yellow one has a vertical side labeled “4cm”, and that same side is the base of the yellow triangle. Since all triangles are right-angled, and the yellow triangle is sitting on top, its right angle is likely at the bottom left corner — meaning the two legs are the vertical 4cm side and the horizontal side going to the right.
And since it’s isosceles, those two legs must be equal → so both legs are 4cm.
Therefore, the three sides of the yellow triangle are:
- Two legs: 4 cm each
- Hypotenuse: √(4² + 4²) = √32 = 4√2 cm
We can leave it as 4√2 cm or approximate it, but since the problem doesn’t specify, exact form is better.
Wait — let me check if there’s any trick here. Are we sure the 4cm is a leg? What if it’s the hypotenuse?
No — because the yellow triangle is drawn such that the 4cm side is adjacent to the right angle (it’s connected to the blue triangle which is also right-angled). Also, if the 4cm were the hypotenuse, then the legs would be shorter, and it wouldn’t make sense with the isosceles condition unless both legs were equal and less than 4cm — but then the diagram wouldn’t match.
Moreover, in the pile-up, each triangle shares a side with the next, and the yellow triangle’s base is clearly the 4cm side from the blue triangle — which is a leg of the blue triangle, and thus becomes a leg of the yellow triangle.
Also, the problem says “Work out the length of its sides” — plural — so we need all three.
Final confirmation: Right-angled isosceles triangle → legs equal → both 4cm → hypotenuse = 4√2 cm.
✔ Verified.
Final Answer:
The yellow triangle has two sides of 4 cm each and a hypotenuse of $ 4\sqrt{2} $ cm.
Parent Tip: Review the logic above to help your child master the concept of pythagoras worksheet.
