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Chapter 3: Q65. (page 301)

Suppose a right triangle has legs of lengths a and b and a

hypotenuse of length h and that this triangle is changing

size, so that the length of its hypotenuse does not change.

Prove that the ratio of the rates of change dadtand dbdtis equal to -ba.

Short Answer

Expert verified

dadtdbdt=-ba

Step by step solution

01

Step 1. Given Information

The length of the two sides of a right-angle triangle is "a"&"b"

and the length of its hypotenuse is"h".

02

Step 2. Calculation

By Pythagora's theorem

h2=a2+b2

Differentiating both sides with respect to"t"we get

2adadt+2bdbdt=0, since hypotenuse remains constant.

or, adadt=-bdbdt

Therefore,dadtdbdt=-ba

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