Question

3.11.13-Setup & Solve The legs of an isosceles right triangle increase in length at a rate of 6 m/s. a. At what rate is the area of the triangle changing when the legs are 5 m long? b. At what rate is the area of the triangle changing when the hypotenuse is 6 m long? c. At what rate is the length of the hypotenuse changing? a. Write an equation relating the area of an isosceles right triangle, A, and the length of the legs of the triangle, X.

Answer 1

L А √x²+x² √2x² = √2x AB. BC Loceles right triangle is shown above with legs Hypotuuse ha Area of Triangle A = 2 x² (x2) h / Ź XX - = 5m A a) Rate of change of a when x = ग d at at dx dt 2:2x. dx 2.dx dt dt Answer i du 6 m/s dt da when a=5m (5).6 = 30 m/s = : dt is om 6) Rate of change of area when hypothuse when hypotmuse h=6 Z x = 6 x = 6/12 : Late x da dt 36. 6.6 h-6 dt DA 36 = 25.46 mis Ansues 12 1.414 At what nate is length of Hypothuse changing Hypotmuse h = 52x ch √2 √3 x 6 6(1.414) = 8.484 ms. c) dt Answar