Mathematics
Assertion (A): In the figure, △ ABC is right angled at B.
Reason (R): In a right angled triangle, the square on the hypotenuse is equal to the sum of the other two sides.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false.
Answer
We know that,
In a right angled triangle, the square on the hypotenuse is equal to the sum of the squares of the other two sides.
∴ Reason (R) is false.
From figure,
Choose the greatest length. Check whether the square of greatest length is equal to the sum of squares of other two lengths.
Here greatest length is 10 cm and other lengths are 8 cm, 6 cm.
Note that 102 = 100 and 82 + 62 = 64 + 36 = 100.
Thus, 102 = 82 + 62
⇒ Hypotenuse2 = Perpendicular2 + Base2
⇒ AC is the hypotenuse and triangle ABC is right angled at B.
∴ Assertion (A) is true.
Hence, Option 1 is the correct option.
Related Questions
There are two buildings in two sides of a road. Keeping the foot of a ladder fixed at a point on the road, when it is placed on two buildings, then its top touches the buidings respectively at a height of 48 ft and 14 ft. If the length of the ladder is 50 ft, then the width of the road is :
56 ft
62 ft
66 ft
70 ft
An aeroplane (P) leaves an Airport (A) and flies towards north at 400 km/h. At the same time another aeroplane (Q) leaves the same airport and flies towards west at 300 km/h.
Based on this information, answer the following questions:
Distance covered by aeroplane P in 1.5 hours is :
(a) 600 km
(b) 650 km
(c) 700 km
(d) 800 kmDistance covered by aeroplane Q in 1.5 hours is :
(a) 600 km
(b) 550 km
(c) 500 km
(d) 450 kmThe distance between the two aeroplanes after a certain period of time is represented by the line segment :
(a) AP
(b) AQ
(c) PQ
(d) ASAfter 1.5 hours, which aeroplane travelled longer distance and by how much?
(a) P, 150 km
(b) Q, 150 km
(c) P, 600 km
(d) Q, 450 kmAfter 1.5 hours, the distance between the two aeroplanes is :
(a) 600 km
(b) 650 km
(c) 700 km
(d) 750 km
Assertion (A): In a right angled triangle, the longest side is called hypotenuse and the other two sides are called its legs. Also, the sum of lengths of legs is less than the length of the hypotenuse.
Reason (R): In a right angled triangle, the side opposite to the right angle is called its hypotenuse.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false.
The hypotenuse of a right triangle is 25 cm. If out of the two legs, one is longer than the other by 5 cm, then the sum of the lengths of the legs is:
30 cm
35 cm
40 cm
45 cm