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4 years ago

In right triangle ABC, angle C = 90 degrees, c = 3, and a + b = square root of 17. Compute the area of the triangle.

Mathematics

1 answer:

Klio2033 [76]4 years ago

4 0

Answer:

Step-by-step explanation:

Given in the question,

a + b = √17

(a+b)² = 17

a² + b² +2ab = 17

a² + b² = 17 - 2ab

<h3>Area of triangle </h3>

1/2 (h)(b)

here h is perpendicular height of triangle = a

b is the base of triangle = b

<h3>Use pythagorus theorem:</h3>

hypotenuse² = base² + height²

3² = a² + b²

9 = a² + b²

9 = 17 - 2ab

9 - 17 = -2ab

-8 = -2ab

cancel minus on both sides

8 = 2ab

ab = 8/2

ab = 4

Plug ab in the formula of area

1/2 (h)(b)

1/2 (a)(b)

1/2 (4)

4/2

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