A large window has the shape of a rectangle surmou

Question

A large window has the shape of a rectangle surmounted by an equilateral triangle.If the perimeter of the window is 12 metres find the dimensions of the rectangle that will produce the largest area of the window.

Rinkoo Gupta · Accepted Answer

let the width and length of rectangle are y and x respectively .each sides of the triangle will be x.so Total area of window S = area of rectangle +area of trianle=xy+(sqrt3)/4 .x2and total perimeter 3x+2y=12 =>y=(12-3x)/2S= x(12-3x)/2 +sqrt3/4.x2=6x+(sqrt3/4 -3/2) x2ds/dx=6+2(sqrt3/4 -3/2 ) xput ds/dx=0then we get x=12/(6-sqrt3)=4(6+sqrt3)/11d2s/dx2=2(sqrt3/4 -3/2) <0so S ios maxima at x=4(6+sqrt3)/11hence x=4(6+sqrt3)/11 and y=12- 12(6+sqrt3)/11=12(5-sqrt3)/11Hence the dimensions of the rectangle are 4(6+sqrt3)/11, 12(5-sqrt3)/11Thanks & RegardsRinkoo GuptaAskIITians Faculty

Differential Calculus> A large window has the shape of a rectang...

A large window has the shape of a rectangle surmounted by an equilateral triangle.If the perimeter of the window is 12 metres find the dimensions of the rectangle that will produce the largest area of the window.

taniska , 11 Years ago

Rinkoo Gupta

Arun Kumar

LIVE ONLINE CLASSES

the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution to move once over to level a playground. find the area of the playground in square m?

differential calculus

Find dy/DX when y=x^sinx+sin-1√x.

Please give me the solution of this problem.

differential calculus

If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.

differential calculus

Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.

differential calculus

Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin C
where A + B + C = T
(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.

differential calculus

Differential Calculus> A large window has the shape of a rectang...

A large window has the shape of a rectangle surmounted by an equilateral triangle.If the perimeter of the window is 12 metres find the dimensions of the rectangle that will produce the largest area of the window.

taniska , 11 Years ago

Rinkoo Gupta

Arun Kumar

LIVE ONLINE CLASSES

Other Related Questions on differential calculus

the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution to move once over to level a playground. find the area of the playground in square m?

differential calculus

Find dy/DX when y=x^sinx+sin-1√x. Please give me the solution of this problem.

differential calculus

If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.

differential calculus

Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.

differential calculus

Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin Cwhere A + B + C = T(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.

differential calculus

Find dy/DX when y=x^sinx+sin-1√x.

Please give me the solution of this problem.

Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin C
where A + B + C = T
(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.