Answer:
A = 210 cm^3
Explanation:
We know that the perimeter of the triangle is the sum of the length of all of it's sides, and that this value equals 70cm. Hence:
70 = (3x-1) + (4x+1) + (3x)
Since we are adding all the terms inside the brackets together, expanding the brackets will not change any of the sides, as we are simply multiplying by 1. This means it can be written like this:
70 = 3x - 1 + 4x + 1 + 3x
Which can be simplified to:
70 = 10x
∴ x = 7 ← dividing by 10 on both sides.
Now we can use the area formula for a triangle to solve for the area:
A = 1/2 × b × h
A = 1/2 × 3x × (3x-1) ← substituting the values given for h and b
A = 1/2 × 3(7) × (3(7) - 1) ← replacing x's with the solution found above
A = 1/2 × 21 × 20
A = 210 cm^3
Hope that helps!