Question

The area of the outer square with sides (a+b) is (a² + 2ab + b²). The sum of the areas of the four triangles with legs (a) and (b) added to the area of the square with side (c) is (? ).

a. (a² + 2ab + b² + c)
b. (2ab + c)
c. (a² + b² + c)
d. (2ab + c²)

Answer 1

The sum of the areas of the four triangles with legs (a) and (b) can be found by multiplying the base and height of each triangle and then adding them together. The area of the outer square with sides (a+b) is (a² + 2ab + b²). The correct answer is (a² + 2ab + b² + c ).

Step-by-step explanation:

The sum of the areas of the four triangles with legs (a) and (b) can be found by multiplying the base and height of each triangle and then adding them together. Since the height of each triangle is (c), the area of each triangle is 1/2 * a * c. Therefore, the total area of the four triangles is 2 * (1/2 * a * c) + 2 * (1/2 * b * c) = a * c + b * c = c * (a + b).

The area of the outer square with sides (a+b) is (a² + 2ab + b²). The sum of the areas of the triangles added to the area of the square is (a² + 2ab + b²) + (c * (a + b)).

Therefore, the correct answer is (a² + 2ab + b² + c).