When providing the pythagorean theorem , we use the given diagram. what is the area of all four triangles combines ?

OPTION B) 2ab

Step-by-step explanation:

Given:

Side of larger square = (a + b) units

Side of smaller square = c units

To Find:

The area of all four triangles combined = ?

Solution:

a^2 + b^2 = c^2       (Pythagoras theorem) -(1)

The area of all four triangles combined = Area of larger square - Area of smaller square

The area of all four triangles combined = (a + b)^2 - c^2

The area of all four triangles combined = a^2 + b^2 + 2ab - (a^2 + b^2)    {By (1)}

The area of all four triangles combined = a^2 + b^2 + 2ab - a^2 - b^2

The area of all four triangles combined = a^2 - a^2 + b^2 - b^2 + 2ab

Therefore, The area of all four triangles combined = 2ab sq. units

OPTION B) 2ab

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step-by-step explanation: lol

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500