Question

the area of ​​the triangle intended by the image below is ... cm².
A. 150
B. 250
C. 300
D. 500​

Answer 1

Answer:

ans is 150

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Answer 2

The area of the triangle intended by the image below is 150 cm.

Discussion

Pythagorean Theorem :-

In a right triangle the pythagorean theorem applies: '' The square of the hypotenuse (hypotenuse) is equal to the sum of squares of the right side ''.

If a triangle with sides a, b, and c is a hypotenuse, then apply :

c² = a² + b² => c = √a² + b²

a² = c² - b² => a² = √c² - b²

b² = c² - a² => b² = √c² - a²

↓↓↓↓↓

Known:

a = 3x cm

b = 20 cm

c = hypotenuse = 5x cm

Asked: The area of a triangle?

Answer :

First we look for the sides of a and c using the pythagorean theorem, with c = hypotenuse:

            c² = a² + b²

       (5x )² = (3x) ² + 20²

         25x² = 9x² + 400

  25x² - 9x² = 400

         16x² = 400

             x² = 400/16

             x² = 25 cm

             x = √25

             x = 5 cm

Enter x = 25 to sides a and b to find the length of each side.

a = 3x

a = 3. 5

a = 15 cm

b = 5x

b = 5. 5

b = 25 cm

Area of a triangle :

L = a × height / 2

L = 15 × 20/2

L = 15 × 10

L = 150 cm²

So, the area of the triangle is 150 cm².