Consider the right triangle below. 6x - 44
2x - 20
3x + 24
If the perimeter of the triangle is 224 cm, find the area of the triangle.
The area of the triangle is
cm

Area = 1,344 cm²

Step-by-step explanation:

First, find the value of x and the numerical side length of all sides of the triangle before finding the area.

Thus:

Perimeter of a triangle = sum of all its side

Therefore,

(6x - 44) + (2x - 20) + (3x + 24) = 224

Solve for x

6x - 44 + 2x - 20 + 3x + 24 = 224

Add like terms

11x - 40 = 224

Add 40 to both sides

11x = 224 + 40

11x = 264

Divide both sides by 11

x = 24

Find the measurement of each side length by plugging in the value of x:

Hypotenuse = 6x - 44 = 6(24) - 44 = 100 cm

Height = 2x - 20 = 2(24) - 20 = 28 cm

Base = 3x + 24 = 3(24) + 24 = 96 cm

Find the area:

Area = ½×base×height

Plug in the values

= ½×96×28

Area = 1,344 cm²

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hope this !