Page 178 - Start Up Mathematics_7

8. Find the length of the unknown sides in the following right-angled triangles:

10 cm x 15 cm
(a) 6 cm (b) 15 cm (c) 24 cm x (d) x

12 cm
8 cm
x 7 cm
9. Find the unknown length in the given figure.

50 m 50 m
14 m

x
10. A 13 m long ladder when set against the wall of a house reaches a height of 12 m. How far
is the foot of the ladder from the wall?
11. 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.
12. A man goes 30 km due north and then 40 km due east. How far away is he from his initial
position?
13. Using Pythagoras theorem, find the length of the second diagonal of a rhombus of side
5 cm and having one of its diagonal as 8 cm.
14. If the square of the hypotenuse of an isosceles right-angled triangle is 242 sq. cm., find the
length of each of the other two sides of the triangle.

At a Glance

1. A triangle has six elements, i.e., 3 sides and 3 angles.

2. (a) Classification according to sides (b) Classification according to angles
Scalene triangle All sides different Acute-angled triangle All angles less than 90°
Isosceles triangle Two sides equal Right-angled triangle One angle equal to 90°
Equilateral triangle All sides equal Obtuse-angled One angle greater than
triangle 90°
3. The medians of a triangle meet at a common point known as the centroid.

4. The altitudes of a triangle are concurrent (i.e., they meet at a point). This point is known as
the orthocentre.
5. Exterior angle theorem: The exterior angle of a triangle is equal to the sum of its two interior
opposite angles.
6. Angle sum property of a triangle: The sum of the three angles of a triangle is 180°.

7. The sum of the lengths of any two sides of a triangle is always greater than the third side and
the difference between the lengths of any two sides is smaller than the third side.

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