RS Aggarwal Class 7 Math Fifteenth Chapter Properties of Triangles Exercise 15D Solution

RS Aggarwal Class 7 Math Fifteenth Chapter Properties of Triangles Exercise 15D Solution

EXERCISE 15D

(1) Find the length of the hypotenuse of a right triangle, the other two sides of which measure 9 cm and 12 cm.

Solution: By Pythagoras’s theorem,

AB² = BC² + AC²

or, AB² = 9² + 12²

or, AB² = 81 + 144

or, AB² = 225

or, AB = √225 = 15

Hence, the length of hypotenuse is 15 cm.

(2) The hypotenuse of a right triangle is 26 cm long. If one of the remaining two sides is 10 cm long, find the length of the other side.

(3) The length of one side of a right triangle is 4.5 cm and the length of its hypotenuse is 7.5 cm. Find the length of its third side.

(4) The two legs of a right triangle are equal and the square of its hypotenuse is 50.Find the length of each leg.

(5) The sides of a triangle measure 15 cm, 36 cm and 39 cm. Show that it is a right-angled triangle.

(6) In right ∆ABC, the lengths of its legs are given as a = 6 cm and b = 4.5 cm. Find the length of its hypotenuse.

(7) The lengths of the sides of some triangles are given below. Which of them are right-angled?

(i) a = 15 cm, b = 20 cm and c = 25 cm

(ii) a = 9 cm, b = 12 cm and c = 16 cm

(iii) a = 10 cm, b = 24 cm and c = 26 cm

(8) In a ∆ABC, ∠B = 35^o and ∠C = 55^o. Write which of the following is true:

(i) AC² = AB² + BC²

(ii) AB² = BC² + AC²

(iii) BC² = AB² + AC²

(9) A 15-m- long ladder is placed against a wall to reach a window12 m high. Find the distance of the foot of the ladder from the wall.

(10) A 5-m-long ladder when set against the wall of a house reaches a height of 4.8 m. How far is the foot of the ladder from the wall?

(11) A tree is broken by the wind but does not separate. If the point from where it breaks is 9 m above the ground and its top touches the ground at a distance of 12 m from its foot, find out the total height of the tree before it broke.

(12) Two poles, 18 m and 13 m high, stand upright in a playground. If their feet are 12 m apart, find the distance between their tops.

(13) A man goes 35 m due west and then 12 m due month. How far is he from the starting point?

(14) A man goes 3 km due north and then 4 km due east. How far is he away from his initial position?

(15) Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.

(16) Find the perimeter of the rectangle whose lengths is 40 cm and a diagonal is 41 cm.

(17) Find the perimeter of  a rhombus, the lengths of whose diagonals are 16 cm and 30 cm.

(18) Fill in the blanks:

(i) In a right angle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

(ii) If the square of one side of a triangle is equal to the sum of the squares of the other two sides then the triangle is right-angled.

(iii) Of all the line segments that can be drawn to a given line from a given point outside it, the perpendicular is the shortest.