
Sufy M.
asked 10/28/20Dont really understand can someone break it down please
The height of a triangle is increasing at a rate of 2.5 centimeters/minute while the area of the triangle is increasing at a rate of 5 square centimeters per minute. At what rate is the base of the triangle changing when the height is 7.5 centimeters and the area is 90 square centimeters?
Remember that you're using the formula for the area of a triangle: Area = 1/2b⋅h
2 Answers By Expert Tutors

Patrick B. answered 10/28/20
Math and computer tutor/teacher
Area = (1/2) base * height
A = (1/2) B * h
dA/dt = (1/2) [ B * dh/dt + dB/dt * h]
dh/dt = 2.5, dA/dt = 5;
wish to find dB/dt
90 = (1/2)*B * 7.5
180 = 7.5 * B
1800 = 75B
B = 1800/75 = 24
5 = (1/2) [ 24 * 2.5 + dB/dt * 7.5 ]
10 = 60 + dB/dt* 7.5
-50 = 7.5 * dB/dt
-6 + 2/3 = dB/dt
Tom K. answered 10/28/20
Knowledgeable and Friendly Math and Statistics Tutor
If A = 1/2 bh, b= 2A/h
Thus, db/dt = (2h dA/dt - 2A dh/dt)/h2
h = 7.5
A = 90
dh/dt = 2.5
dA/dt = 5
Thus, db/dt = (2*7.5 * 5 - 2 * 90 * 2.5)/7.52 = -20/3 cm/sec or-6 2/3 cm/sec
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Patrick B.
well there ya go Sufy... 2 different tutors... same answer10/28/20