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.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654.png)
(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.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-1.png)
(4) The two legs of a right triangle are equal and the square of its hypotenuse is 50.Find the length of each leg.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-2.png)
(5) The sides of a triangle measure 15 cm, 36 cm and 39 cm. Show that it is a right-angled triangle.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-3.png)
(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.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-4.png)
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-5.png)
(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
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-6.png)
(ii) a = 9 cm, b = 12 cm and c = 16 cm
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-7.png)
(iii) a = 10 cm, b = 24 cm and c = 26 cm
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-8.png)
(8) In a ∆ABC, ∠B = 35o and ∠C = 55o. Write which of the following is true:
(i) AC2 = AB2 + BC2
(ii) AB2 = BC2 + AC2
(iii) BC2 = AB2 + AC2
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-9.png)
(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.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-10.png)
(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?
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-11.png)
(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.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-12.png)
(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.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-13.png)
(13) A man goes 35 m due west and then 12 m due month. How far is he from the starting point?
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-14.png)
(14) A man goes 3 km due north and then 4 km due east. How far is he away from his initial position?
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-15.png)
(15) Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-16.png)
(16) Find the perimeter of the rectangle whose lengths is 40 cm and a diagonal is 41 cm.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-17.png)
(17) Find the perimeter of a rhombus, the lengths of whose diagonals are 16 cm and 30 cm.
![](https://www.netexplanations.com/wp-content/uploads/2018/10/489756545554654-18.png)
(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.
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