Advertisements
Advertisements
प्रश्न
Identify, with reason, if the following is a Pythagorean triplet.
(4, 9, 12)
Advertisements
उत्तर
In the triplet (4, 9, 12),
42 = 16, 92 = 81, 122 = 144 and 16 + 81 = 97 ≠ 144
The square of the largest number is not equal to the sum of the squares of the other two numbers.
∴ (4, 9, 12) is not a pythagorean triplet.
APPEARS IN
संबंधित प्रश्न
PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.
Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.
Prove that, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of remaining two sides.
Identify, with reason, if the following is a Pythagorean triplet.
(5, 12, 13)
AD is drawn perpendicular to base BC of an equilateral triangle ABC. Given BC = 10 cm, find the length of AD, correct to 1 place of decimal.
In figure AB = BC and AD is perpendicular to CD.
Prove that: AC2 = 2BC. DC.
M andN are the mid-points of the sides QR and PQ respectively of a PQR, right-angled at Q.
Prove that:
(i) PM2 + RN2 = 5 MN2
(ii) 4 PM2 = 4 PQ2 + QR2
(iii) 4 RN2 = PQ2 + 4 QR2(iv) 4 (PM2 + RN2) = 5 PR2
Prove that `(sin θ + cosec θ)^2 + (cos θ + sec θ)^2 = 7 + tan^2 θ + cot^2 θ`.
The sides of a certain triangle is given below. Find, which of them is right-triangle
6 m, 9 m, and 13 m
In the right-angled ∆LMN, ∠M = 90°. If l(LM) = 12 cm and l(LN) = 20 cm, find the length of seg MN.
A man goes 10 m due east and then 24 m due north. Find the distance from the straight point.
In ΔABC, AD is perpendicular to BC. Prove that: AB2 + CD2 = AC2 + BD2
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 = AD2 + BC x DE + `(1)/(4)"BC"^2`
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 - AB2 = 2BC x ED
AD is perpendicular to the side BC of an equilateral ΔABC. Prove that 4AD2 = 3AB2.
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?
The hypotenuse of a right angled triangle of sides 12 cm and 16 cm is __________
If ΔABC ~ ΔPQR, `("ar" triangle "ABC")/("ar" triangle "PQR") = 9/4` and AB = 18 cm, then the length of PQ is ______.
Sides AB and BE of a right triangle, right-angled at B are of lengths 16 cm and 8 cm respectively. The length of the side of largest square FDGB that can be inscribed in the triangle ABE is ______.
In an isosceles triangle PQR, the length of equal sides PQ and PR is 13 cm and base QR is 10 cm. Find the length of perpendicular bisector drawn from vertex P to side QR.
