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For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the angle between the hypotenuse and the side is

For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the angle between the hypotenuse and the side is Correct Answer 60°

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The following questions are accompanied by three statements (I), (II) and (III). You have to determine which statement(s) is/are sufficient/necessary to answer the questions. Perpendicular and base of a right-angle triangle are 5x and 12x respectively. Find the area of right-angled triangle. I. Perimeter of the right-angle triangle is p cm.  II. Length of the diagonal side is d cm. III. Area of another triangle similar to given triangle is 300 cm2.
The following questions are accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. Perpendicular and base of a right-angle triangle are 5x and 12x respectively. Find the area of right-angled triangle. I. Perimeter of the right-angle triangle is p cm.  II. Length of the diagonal side is d cm. III. Area of another triangle similar to the given triangle is 300 cm2.
Six boxes containing different items namely, Copy, Pen, pencil, Scissor, Tape and Paper, are kept in a straight line, one after the other, not necessarily in the same order. The box of Pen is kept at the third position in the line from the left end. The box of Paper is kept at the extreme right end. The box of Pencil is kept somewhere between box of pen and box of paper. The box of Tape is kept at the left of the box of Pen but at the right of the box of Copy, when counting from the left end. The box of scissor is not kept immediately next to Paper. Which box is kept at the second position from the right end?
Two right angled triangles are congruent if :
I. The hypotenuse of one triangle is equal to the hypotenuse of the other.
II. A side for one triangle is equal to the corresponding side of the other.
III. Sides of the triangles are equal.
IV. An angle of the triangle are equal.
Of these statements, the correct ones are combination of:
Eight articles A1, A2, A3, A4, A5, A6, A7 and A8 are kept one above the other, (not necessarily in the same order). Number of articles between A3 and A5 are two. A3 is kept below A5. A8 is just below A7. Only one article is kept between A6 and A1. A6 is kept above A1. A7 and A8 are between A3 and A5. Three articles are kept between A6 and A7. A7 is kept above A6. Which of the following statements is correct about A4?
Eight articles A1, A2, A3, A4, A5, A6, A7 and A8 are kept one above the other, (not necessarily in the same order). Number of articles between A3 and A5 are two. A3 is kept below A5. A8 is just below A7. Only one article is kept between A6 and A1. A6 is kept above A1. A7 and A8 are between A3 and A5. Three articles are kept between A6 and A7. A7 is kept above A6. Which of the following statement is correct about A4?
The cages of five animals, Lion, Tiger, Elephant, Giraffe and Zebra were kept in a line one after the other, not necessarily in the same order. Lion’s cage is not kept at the last and giraffe’s cage is not kept at the first. Tiger’s cage was kept at the centre of the line. Zebra’s cage was kept after Lion’s but before Tiger’s cage. There was one cage kept between Tiger’s and Giraffe’s cage. Whose cage is kept at the last in the line?
The hypotenuse of a right-angled triangle 10 cm and its area is 24 cm^2. If the shorts side is halved and the longer side is double, the new hypotenuse becomes
In a right angled triangle if one side forming the right angle is 6 and the hypotenuse is 10. What is the length of the other right angle forming side?
The hypotenuse of a right triangle is 2 centimeters more than linger side of the triangle. The shorter side of the triangle is 7 centimeters less than the longer side. Find the length of the hypotenuse.