Answer: The base of the triangle is decreasing at the rate of 2.16cm per minute
Explanation:
The area of a triangle is = 1/2 base × height.
We would make use of the product rule to find the rate of change of the base of this triangle.
Let us use A to represent the area, h to represent height, and b to represent base.
dA/dt = [(1/2) × (dh/dt) × b] + [(1/2) × (db/dt) × h]
Where:-
dh/dt = 1.5, dA/dt = 1.5, h = 10, db/dt = the unknown.
Before proceeding further, we must find the base of the triangle. Since we already know that the height = 10cm and the area = 82 square centimeters. We can find the base.
Formula for area of a triangle is 1/2 × b × h = A.
We substitute accordingly: 1/2 × b × 10 = 82.
10b/2 = 82
10b = 164
b = 16.4cm
Since the base is 16.4cm, we can calculate the rate of change of the base of the triangle (db/dt) using the product rule formula stated earlier on.
1.5 = [(1/2) × (1.5) × (16.4)] + [(1/2) × (db/dt) × (10)]
1.5 = (1.5 × 8.2) + (db/dt × 5)
1.5 = (12.3) + (db/dt × 5)
db/dt × 5 = 1.5 - 12.3
db/dt × 5 = -10.8
db/dt = -10.8/5
db/dt = -2.16cm/min
Therefore, the base of the triangle is decreasing at the rate of 2.16cm per minute