Advertisements
Advertisements
प्रश्न
Each side of rhombus is 10cm. If one of its diagonals is 16cm, find the length of the other diagonals.
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
The diagonal of a rectangular field is 16 metres more than the shorter side. If the longer side is 14 metres more than the shorter side, then find the lengths of the sides of the field.
Sides of triangle are given below. Determine it is a right triangle or not? In case of a right triangle, write the length of its hypotenuse. 7 cm, 24 cm, 25 cm
In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AB2 = BC × BD
Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.
Which of the following can be the sides of a right triangle?
2 cm, 2 cm, 5 cm
In the case of right-angled triangles, identify the right angles.
A ladder 13 m long rests against a vertical wall. If the foot of the ladder is 5 m from the foot of the wall, find the distance of the other end of the ladder from the ground.
In the following figure, OP, OQ, and OR are drawn perpendiculars to the sides BC, CA and AB respectively of triangle ABC.
Prove that: AR2 + BP2 + CQ2 = AQ2 + CP2 + BR2
In triangle PQR, angle Q = 90°, find: PR, if PQ = 8 cm and QR = 6 cm
Find the Pythagorean triplet from among the following set of numbers.
4, 7, 8
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 = AD2 - BC x CE + `(1)/(4)"BC"^2`
In a right-angled triangle PQR, right-angled at Q, S and T are points on PQ and QR respectively such as PT = SR = 13 cm, QT = 5 cm and PS = TR. Find the length of PQ and PS.
∆ABC is right-angled at C. If AC = 5 cm and BC = 12 cm. find the length of AB.
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 __________
In the figure, find AR
From given figure, In ∆ABC, If AC = 12 cm. then AB =?
Activity: From given figure, In ∆ABC, ∠ABC = 90°, ∠ACB = 30°
∴ ∠BAC = `square`
∴ ∆ABC is 30° – 60° – 90° triangle
∴ In ∆ABC by property of 30° – 60° – 90° triangle.
∴ AB = `1/2` AC and `square` = `sqrt(3)/2` AC
∴ `square` = `1/2 xx 12` and BC = `sqrt(3)/2 xx 12`
∴ `square` = 6 and BC = `6sqrt(3)`
In the given figure, ∠T and ∠B are right angles. If the length of AT, BC and AS (in centimeters) are 15, 16, and 17 respectively, then the length of TC (in centimeters) is ______.
Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides of the triangle.
Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures 60 metres × 80 metres. How much shorter is the route across the park than the route around its edges?
