A triangle has a base that is increasing at a rate of 18 mm per minute with the height being held constant. What is the rate of

Question

3 years ago

15

change of the area of the triangle if the height is 7 mm

1 answer:

fomenos · Answer 1 · 2022-01-29T15:08:47+03:00

Answer:

Step-by-step explanation:

Area of a triangle = 1/2 * base * height

A = 1/2bh

Rate of change of area is expresssed as dA/dt = dA/db * db/bt

db/dt is the rate at which the base is increasing.

Given db/dt = 18mm/min

A = 1/2*7b

A = 7b/2

dA/db = 7/2

The rate at which the area is changing dA/dt = dA/db * db/bt

dA/dt = 7/2 * 18

dA/dt = 7*9

dA/dt = 63mm/min

<em>Hence the rate at which the area of the triangle is changing is 63mm/min </em>