Mensuration Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts

Question : 26

The hypotenuse of a right triangle is 3$√10$ unit. If the smaller side is tripled and the longer side is doubled, new hypotenuse becomes 9$√5$ unit. What are the lengths of the smaller and longer sides of the right triangle, respectively?

a) 3 and 9 units

b) 5 and 9 units

c) 5 and 6 units

d) 3 and 6 units

Question : 27

If the length of the hypotenuse of a right angled triangle is 10 cm, then what is the maximum area of such a right angled triangle ?

a) 25 cm$^2$

b) 100 cm$^2$

c) 50 cm$^2$

d) 10 cm$^2$

Question : 28

If area of a circle and a square are same, then what is the ratio of their perimeters ?

a) $√π/2$

b) 2 $√π$

c) $√π$

d) $√π/4$

Question : 29

Which one of the following is a Pythagorean triple in which one side differs from the hypotenuse by two units?

a) ($2n^2$ , 2n, 2n + 1)

b) (2n + 1, 4n, $2n^2$ + 2n)

c) (2n, 4n, $n^2$ + 1)

d) (2n, $n^2$ – 1, $n^2$ + 1) Where, n is a positive real number.

Question : 30

A circle of radius r is inscribed in a regular polygon with n sides (the circle touches all sides of the polygon). If the perimeter of the polygon is p, then the area of the polygon is

a) ${pr}/2$

b) (p + n) r

c) (2p – n) r

d) None of the above