Expanding isosceles triangle The legs of an isosceles right tri- angle increase in length at a rate of 2 m/s. a. At what rate is the area of the trian

tabita57i

tabita57i

Answered question

2020-12-13

Expanding isosceles triangle The legs of an isosceles right tri- angle increase in length at a rate of 2 m/s.
a. At what rate is the area of the triangle changing when the legs are 2 m long?
b. At what rate is the area of the triangle changing when the hypot- enuse is 1 m long?
c. At what rate is the length of the hypotenuse changing?

Answer & Explanation

Jozlyn

Jozlyn

Skilled2020-12-14Added 85 answers

Consider a isosceles right triangle ABC,
image
Consider AB = x is the length of a leg of a isosceles right triangle an AC = y is a hypotenuse. Given that,  dx  dt =2 m/s
a) We know that area of a right triangle =12× base × height
A=12(x)(x)
A=12x2 (1)
Differentiate A with respect to t,
dA dt =d dt (12x2)
dA dt =12(2x) dx  dt 
dA dt =x dx  dt (2)
dA dt =(2)(2) [Given]
dA dt =4
Hence area of the triangle changing at 4m2s.
b) In isosceles right triangle ABC,
AC2=AB2+BC2 [Using pythoras theorem]
y2=x2+x2
y2=2x2
1=2x2 [Given that hypotenuse y=1m]
x2=12
x=12
Substtute x=12 and  dx  dt =2 in (2)
dA dt =(12)(2)
dA dt =2
Hence area of the triangle changing at 2m2/s.
c) In isosceles right triangle ABC,
AC2=AB2+BC2 [Using pythoras theorem]
y2=x2+x2
y2=2x2
y=2x
Differentiate y with respect to t,
 dy  dt =d dt (2x)
 

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