Question

The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the triangle is increasing at a rate of 4 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8 centimeters and the area is 82 square centimeters?

Answer 1

we know that area of a triangle is given by,

where b is the base of a triangle and h is the height(altitude) of a triangle

we can write,

----------------------------------------------------1)

we have to find the rate of change of base means db/dt when altitude is 8 centimeters and the area is 82 square centimeters given that the  altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the triangle is increasing at a rate of 4 square centimeters/minute

It means we have,

h = 8 cm, A = 82 square cm

dh/dt = 3 cm per minute and dA/dt = 4 cm per minute

we know that,

Hence we can write,

we have h = 8 and A = 82 hence,

Put b = 20.5, h = 8 , A = 82, dh/dt = 3 and dA/dt = 4 in equation 1) we can write,

minus sign indicates that base is decreasing

Hence we can write base of a triangle is changing at a rate of -6.6875 cm per minute

we can also write base of a triangle is decreasing at a rate of 6.6875 cm per minute

we can also write,