Answer:
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
