Advertisements
Advertisements
प्रश्न
Each side of rhombus is 10cm. If one of its diagonals is 16cm, find the length of the other diagonals.
Advertisements
उत्तर
Side of the rhombus = 10cm
One diagonal, d1 = 16cm
Let d2 be the other diagonal of the rhombus
The diagonals of a rhombus bisect each other
∴ `("d"_1/2)^2 + ("d"_2/2)^2` = side2
`8^2 + ("d"_2/2)^2` = 100
⇒ `("d"_2/2)^2` = 100 - 64 = (6)2
⇒ `("d"_2)/(2^2)` = 6
⇒ d2 = 12
Thus, the other diagonal of the rhombus is of length 12cm.
APPEARS IN
संबंधित प्रश्न
Prove that the diagonals of a rectangle ABCD, with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6), are equal and bisect each other.
In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AB2 = BC × BD
A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?
Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, ho much string does she have out (see Figure)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?
A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.
Identify, with reason, if the following is a Pythagorean triplet.
(3, 5, 4)
ABC is a triangle, right-angled at B. M is a point on BC.
Prove that: AM2 + BC2 = AC2 + BM2
Diagonals of rhombus ABCD intersect each other at point O.
Prove that: OA2 + OC2 = 2AD2 - `"BD"^2/2`
O is any point inside a rectangle ABCD.
Prove that: OB2 + OD2 = OC2 + OA2.
A ladder, 6.5 m long, rests against a vertical wall. If the foot of the ladder is 2.5 m from the foot of the wall, find up to how much height does the ladder reach?
The sides of the triangle are given below. Find out which one is the right-angled triangle?
40, 20, 30
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2AD2 + `(1)/(2)"BC"^2`
In a square PQRS of side 5 cm, A, B, C and D are points on sides PQ, QR, RS and SP respectively such as PA = PD = RB = RC = 2 cm. Prove that ABCD is a rectangle. Also, find the area and perimeter of the rectangle.
Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of `(20 "km")/"hr"` and the second train travels at `(30 "km")/"hr"`. After 2 hours, what is the distance between them?
If in a ΔPQR, PR2 = PQ2 + QR2, then the right angle of ∆PQR is at the vertex ________
In the figure, find AR
From the given figure, in ∆ABQ, if AQ = 8 cm, then AB =?
In an equilateral triangle PQR, prove that PS2 = 3(QS)2.
Two squares are congruent, if they have same ______.
The hypotenuse (in cm) of a right angled triangle is 6 cm more than twice the length of the shortest side. If the length of third side is 6 cm less than thrice the length of shortest side, then find the dimensions of the triangle.
