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
From a point O in the interior of a ∆ABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove
that :
`(i) AF^2 + BD^2 + CE^2 = OA^2 + OB^2 + OC^2 – OD^2 – OE^2 – OF^2`
`(ii) AF^2 + BD^2 + CE^2 = AE^2 + CD^2 + BF^2`
In a right triangle ABC right-angled at C, P and Q are the points on the sides CA and CB respectively, which divide these sides in the ratio 2 : 1. Prove that
`(i) 9 AQ^2 = 9 AC^2 + 4 BC^2`
`(ii) 9 BP^2 = 9 BC^2 + 4 AC^2`
`(iii) 9 (AQ^2 + BP^2 ) = 13 AB^2`
An aeroplane leaves an airport and flies due north at a speed of 1,000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1,200 km per hour. How far apart will be the two planes after `1 1/2` hours?
The perpendicular from A on side BC of a Δ ABC intersects BC at D such that DB = 3CD . Prove that 2AB2 = 2AC2 + BC2.
In an equilateral triangle ABC, D is a point on side BC such that BD = `1/3BC` . Prove that 9 AD2 = 7 AB2
ABC is a triangle right angled at C. If AB = 25 cm and AC = 7 cm, find BC.
In triangle ABC, AB = AC = x, BC = 10 cm and the area of the triangle is 60 cm2.
Find x.
In the following figure, AD is perpendicular to BC and D divides BC in the ratio 1: 3.
Prove that : 2AC2 = 2AB2 + BC2
In the figure, given below, AD ⊥ BC.
Prove that: c2 = a2 + b2 - 2ax.
In equilateral Δ ABC, AD ⊥ BC and BC = x cm. Find, in terms of x, the length of AD.
O is any point inside a rectangle ABCD.
Prove that: OB2 + OD2 = OC2 + OA2.
Triangle ABC is right-angled at vertex A. Calculate the length of BC, if AB = 18 cm and AC = 24 cm.
In the given figure, angle ADB = 90°, AC = AB = 26 cm and BD = DC. If the length of AD = 24 cm; find the length of BC.
Find the Pythagorean triplet from among the following set of numbers.
2, 4, 5
Calculate the area of a right-angled triangle whose hypotenuse is 65cm and one side is 16cm.
The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall to what height does its tip reach?
A point OI in the interior of a rectangle ABCD is joined with each of the vertices A, B, C and D. Prove that OB2 + OD2 = OC2 + OA2
From the given figure, in ∆ABQ, if AQ = 8 cm, then AB =?
The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is ______.
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.
