Page 182 - Maths Skills - 7

180 Maths

3. The length of AB is — Q. 1. Assertion (A): Two sides of a triangle are of the
(i) 12 m (ii) 38 m lengths 5 cm and 1.5 cm. The length of the third
(iii) 50 m (iv) none of these side of the triangle can not be 3.4 cm.

4. The length of rope is — Reason (R): The difference between any two
sides of a triangle should be less than the third
(i) 120 m (ii) 70 m side.
(iii) 82 m (iv) none of these Q. 2. Assertion (A): In ∆ABC, if AB = AC then ∠B = ∠C
5. Which of the following does not form a Reason (R): Two angles of an isosceles triangle
pythagoras triplet? are equal.
(i) (7, 24, 25) (ii) (15, 8, 17) Q. 3. Assertion (A): For a right angled triangle, two

(iii) (5, 12, 13) (iv) (21, 20, 28) altitudes are two sides of this triangle.
Reason (R): The angle opposite to the hypotenuse
E. Assertion-Reason Based Questions in a right angled triangle is the biggest.
Directions for Questions 1 to 3: In each of the
questions given below, there are two statements
marked as Assertion (A) and Reason (R). Mark your SUBJECTIVE TYPE QUESTIONS
answer as per the codes provided below: F. Solve the following word problems
(a) Both A and R are true and R is the correct 1. The square of a diagonal of a square is 98 cm .
2
explanation of A. Find the side of a square.
(b) Both A and R are true but R is not the correct 2. A ladder 15 m long reaches a window which
explanation of A. is 9 m above the ground on one side of a street
(c) A is true but R is false. keeping its foot at the same point, the ladder
(d) A is false but R is true. is turned to other side of the street to reach a
window 12 m high. Find the width of the street.

INTEGRATED QUESTION

G. History Vs Maths
In ancient time, the Nile River annually flooded the lands and destroyed land boundaries. To remake the
boundaries, people had to make a square corner. For this, they used rope stretchers. They took a piece of rope
and made 36 knots with equal spaces. Then they stretched the rope around the three wooden rods to form a
triangle such that the sides of the triangle had lengths of 9, 12 and 15 units.

1. Explain why this method resulted in a square corner?

2. Draw 2 rough sketches to show:

(a) 3 medians in this triangle.
(b) 3 altitudes in this triangle.

3. Could they have used 30 knots instead of 36 to make a right-angle triangle?

4. What other number of knots could they use to make the right-angle triangle? (State any two). What will be
the length of the sides of these triangles?
5. Which other type of triangle can be made using a rope of 30 knots with equal spaces? (Remember that
knots also has to be on the vertices of the triangle).