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Show that a right triangle of given hypo...

Show that a right triangle of given hypotenuse has maximum area, when it is an isosceles triangle.

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Prove that the area of a right-angled triangle of a given hypotenuse is maximum when the triangle is isosceles.

Show that in a right angled triangle, the hypotenuse is the longest side.

Equilateral triangles are drawn on the three sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

If 2cosA=sinB/sinC then show that the triangle is an isosceles triangle

If the sum of the lengths of the hypotenuse and another side of a right-angled triangle is given, show that the area of the triangle is maximum when the angle between these sides is pi/3dot

write the ratio of the angles of a right angled isosceles triangle.

Somen has drawn a right-angled triangle, the hypotenuse of which is 3 cm more the twice of its smallest side. If the length of its third side be 1 cm less than the hypotenuse, then find the lengths of the sides of the right-angled triangle.

Construct a right angled triangled whose hypotenuse is 10cm and aother side is 6.5 cm . Construct incircle of that triangle.

If the sum of the lengths of hypotenuse and a side of a right - angled trianle is given , show that the area of the triangle is maximum when the angle between them is (pi)/(3)

To construct a right angled triangle whose one side and length of hypotenuse is given. In a right angled triangle, One angle has to be square [right angle/obtuse angle]

UNITED BOOK HOUSE-SET 15-EXERCISE
  1. Find if Lagrange's Mean Value Theorem is applicable to the function f...

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  2. Evaluate: int cos(logx)dx.

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  3. Show that a right triangle of given hypotenuse has maximum area, when ...

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  4. Find the interval in which f(x) = sinx + cos x.[x in [0, 2 pi]] increa...

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  5. Evaluate: underset(0)overset(1)int(1/(1+x))dx.

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  6. If vec a, vec b and vec c are such that veca xx vecb = vecc and vecb x...

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  7. Find the angle between the lines vecr = (2hati - hatj +3hatk) + lambda...

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  8. If P(A) = 2P(B) = 2/5 and P(B/A) = 1/3, find P(A/B) and P(AuuB).

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  9. A pair of dice is thrown 3 times. Find the probability of getting a do...

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  10. If tan^(-1) [(yz)/(xr)] + tan^(-1) [(zx)/(yr)]+ tan^(-1) [(xy)/(zr)] =...

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  11. If A = [[1,-1],[2,-1]],B = [[a,1],[b,-1]] and (A+B)^2 = A^2+B^2 find a...

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  12. Prove that, [[1+x,1,1],[1,1+y,1],[1,1,1+z]] = xyz(1 + 1/x+1/y+1/z)

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  13. Solve :[[x-2,2x-3,3x-4],[x-4,2x-9,3x-16],[x-8,2x-27,3x-64]]=0

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  14. If siny = x sin(a+y) then show that (dy)/(dx)= (sina)/(1-2xcos a+x^2).

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  15. Evaluate:int e^(4x)sin 3x dx

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  16. Evaluate:int (tan theta d theta)/(1-sin theta)

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  17. Solve:(x+y+1)dx + (2x+2y-1)dy = 0

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  18. solve:(dy)/(dx) + (sin 2y)/(x) = x^3cos^2y.

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  19. If the vectors a hati + hatj + hatk, hati + b hatj + hatk and hati + h...

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  20. If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx ...

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