the area of a triangle is 124 square units what would it’s new area be if it’s base was half as long and its height was three times as long
If the base of the triangle is halved and the height is tripled, the new area of the triangle can be calculated using the formula for the area of a triangle:
Area = (1/2) * base * height
Let the original base be "b" units and original height be "h" units. The original area of the triangle is given as 124 square units.
Therefore, 124 = (1/2) * b * h
Now, new base = b/2 and new height = 3h. The new area of the triangle can be calculated as:
New Area = (1/2) * (b/2) * (3h)
= (1/2) * (3/2) * b * h
= (3/4) * b * h
Since the original area was 124 square units, we have:
124 = (3/4) * b * h
Now, to find the new area with the halved base and tripled height, plug in the values into the equation:
New Area = (3/4) * (b/2) * (3h)
= (3/4) * (1/2) * b * 3h
= (3/8) * b * 3h
= (9/8) * b * h
Therefore, the new area of the triangle with a base that is half as long and a height that is three times as long would be 9/8 times the original area.
(9/8) * 124 = 139.5 square units
So, the new area of the triangle would be 139.5 square units.