Explanation:
We are given a right triangle with squares built on each of its three sides. The areas of the squares are:
- Square on side
a: area(P) = 16 units²
- Square on side
b: area(Q) = 9 units²
- Square on hypotenuse
c: area(R) = 25 units²
The Pythagorean Theorem says:
> In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
In terms of areas of the squares:
area(P) + area(Q) = area(R)
Let’s check:
16 + 9 = 25 →
✔ True.
Also, since area = side², we can find the side lengths:
- Side
a = √16 = 4
- Side
b = √9 = 3
- Side
c = √25 = 5
Check if they satisfy the Pythagorean identity:
a² + b² = c²
→ 4² + 3² = 16 + 9 = 25 = 5² →
✔ Correct.
So everything is consistent.
The problem seems to be verifying or using the Pythagorean Theorem via areas. Since the question is just to solve the problem (and no specific question like “find a” or “verify” is stated), but the image shows the equation
16 + 9 = 25, and the algebraic form
a² + b² = c², the core result is that the relationship holds.
If the task is to confirm the value of
c², then from the given:
a² = 16, b² = 9 ⇒ c² = 16 + 9 = 25.
Final Answer:
25
Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem using graphs worksheet.
