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Numerade Educator

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Problem 22 Easy Difficulty

The altitude of a triangle is increasing at a rate of $ 1 cm/min $ while the area of the triangle is increasing at a rate of $ 2 cm^2/min. $ At what rate is the base of the triangle changing when the altitude is $ 10 cm $ and the area is $ 100 cm^2? $

Answer

Rate of decrease of distance between boat and dock is $\frac{\sqrt{65}}{8} \approx 1 \mathrm{ms}^{-1}$

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Video Transcript

oh this is a question in which will be using the concept of increasing and decreasing our application of derivative. We should say if this is triangle abc, this is the altitude and this is the base so Area is 1/2 and two. Base into the altitude question number one. Now various things we have been given ah that altitude is increasing at a rate of one centimeter per minute. So D. H by DT is one cm/min. An area is increasing at the rate of two centimeters Squire per minute. So we need to find the raid outfits. The basis is changing when altitude is 10 centimeter and base area and the area is 100 centimeters square. So let us differentiate equation number eight with respect to T so dear by duty is half since be an edge all our variables. So you'll be using the concept of the differentiation of the product. So be the H by DT place DB by DT into at Disability is 2 1 x two B. What should be base should be taken as okay. At what rate is the base of the triangle is changing when altitude? Okay no problem. Be into DHB oddity we have one place delivery T. We need to find out and altitude is 10 cm we have to find the value of B when area is and the centimeter and ah Altitude is 10 cm 8800 centimeter square half into base into altitude 10. So the system. So BB. is 20 cm so we'll be plugging in value of 20 over here. So this will be to equal to one x 2, 22 and 20 plus DB by detained 2 10. So this will be four Equal to 20 plus and D. V by DT So D V. But it will be cool too, -16 x 10 -8 x five. So the rate of change of the base will be minus 85 centimeter permit on minus one point six centimeter per minute. Now this negative science shows that the base is decreasing with time. Thank you.