Advertisements
Advertisements
प्रश्न
Identify, with reason, if the following is a Pythagorean triplet.
(5, 12, 13)
उत्तर
In the triplet (5, 12, 13),
52 = 25,
122 = 144,
132 = 169
52 + 122 = 25 + 144 = 169
The square of the largest number is equal to the sum of the squares of the other two numbers.
∴ (5, 12, 13) is a pythagorean triplet.
APPEARS IN
संबंधित प्रश्न
The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right traingle ,right-angled at B. Find the values of p.
ABC is a right-angled triangle, right-angled at A. A circle is inscribed in it. The lengths of the two sides containing the right angle are 5 cm and 12 cm. Find the radius of the circle
ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2
In the following figure, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that
(i) OA2 + OB2 + OC2 − OD2 − OE2 − OF2 = AF2 + BD2 + CE2
(ii) AF2 + BD2 + CE2 = AE2 + CD2 + BF2
A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.
In the given figure, ∠B = 90°, XY || BC, AB = 12 cm, AY = 8cm and AX : XB = 1 : 2 = AY : YC.
Find the lengths of AC and BC.
Triangle ABC is right-angled at vertex A. Calculate the length of BC, if AB = 18 cm and AC = 24 cm.
In the figure below, find the value of 'x'.
In the figure below, find the value of 'x'.
Find the Pythagorean triplet from among the following set of numbers.
4, 7, 8
The length of the diagonals of rhombus are 24cm and 10cm. Find each side of the rhombus.
In an equilateral triangle ABC, the side BC is trisected at D. Prove that 9 AD2 = 7 AB2.
In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that: 9BP2 = 9BC2 + 4AC2
There are two paths that one can choose to go from Sarah’s house to James's house. One way is to take C street, and the other way requires to take B street and then A street. How much shorter is the direct path along C street?
Choose the correct alternative:
If length of sides of a triangle are a, b, c and a2 + b2 = c2, then which type of triangle it is?
If S is a point on side PQ of a ΔPQR such that PS = QS = RS, then ______.
In the adjoining figure, a tangent is drawn to a circle of radius 4 cm and centre C, at the point S. Find the length of the tangent ST, if CT = 10 cm.
Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is ______.
The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is ______.
The foot of a ladder is 6 m away from its wall and its top reaches a window 8 m above the ground. Find the length of the ladder.
