Advertisements
Advertisements
Question
If the length of diagonal of square is `sqrt(2)`, then what is the length of each side?
Options
2
`sqrt(3)`
1
4
Advertisements
Solution
1
Explanation:
Let ABCD be the given square.
In ∆ABC,
∠B = 90°
∴ AC2 = AB2 + BC2 ...[Pythagoras theorem]
∴ `(sqrt(2))^2 = AB^2 + AB^2` ...[Sides of the square]
∴ 2 = 2AB2
∴ AB2 = 1
∴ AB = 1 unit
APPEARS IN
RELATED QUESTIONS
The hypotenuse of a right triangle is 6 m more than twice of the shortest side. If the third side is 2 m less than the hypotenuse, find the sides of the triangle
5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.
In a ∆ABC, AD is the bisector of ∠BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. The length of the side AC is
Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?
If the sides of a triangle are in the ratio 5 : 12 : 13 then, it is ________
8, 15, 17 is a Pythagorean triplet
The incentre is equidistant from all the vertices of a triangle
Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem
30, 40, 50
Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem
9, 40, 41
Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem
24, 45, 51
In right angled triangle, if sum of the squares of the sides of right angle is 169, then what is the length of the hypotenuse?
A rectangle having length of a side is 12 and length of diagonal is 20, then what is length of other side?
In ∆ABC, AB = `6sqrt(3)` cm, AC = 12 cm, and BC = 6 cm then m∠A = ?
If a triangle having sides 8 cm, 15 cm and 17 cm, then state whether given triangle is right angled triangle or not.
In ΔABC, AB = 9 cm, BC = 40 cm, AC = 41 cm. State whether ΔABC is a right-angled triangle or not. Write reason.
In the given figure, triangle PQR is right-angled at Q. S is the mid-point of side QR. Prove that QR2 = 4(PS2 – PQ2).
