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Chapter 3: Q. 25 (page 299)

In Exercises 19鈥�26, write down an equation that relates the two quantities described. Then use implicit differentiation to obtain a relationship between the rates at which the quantities change over time. The area A and hypotenuse c of an isosceles right triangle.

Short Answer

Expert verified

Equation relating the quantities:A=c24

Implicit differentiation:dAdt=c2dcdt

Step by step solution

01

Step 1. Given information  

Area of isosceles right angled triangle =A

Hypotenuse of isosceles right angled triangle=c

02

Step 2. Equation relating the quantities 

For a isosceles right angled triangle,

(base)2+(height)2=(hyotenuse)2,where,base=heightLet,base=height=b鈬�b2+b2=c2鈬�2b2=c2鈬�b2=c22鈬�b=c2Theareaoftheisoscelesrightangledtriangleisgivenby,A=(base)(height)2鈬�A=c2c22鈬�A=c24

03

Step 3. Implicit differentiation with respect to time

From the above step,

A=c24Differentiatingonbothsides,weget,dAdt=2c4dcdt鈬�dAdt=c2dcdt

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