Advertisements
Advertisements
Question
Digonals of parallelogram WXYZ intersect at point O. If OY =5, find WY.
Advertisements
Solution
WY = 2 OY = 2×5 = 10 cm (Diagonals of parallelogram bisect each other).
APPEARS IN
RELATED QUESTIONS
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`
In Figure ABD is a triangle right angled at A and AC ⊥ BD. Show that AC2 = BC × DC

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals
In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.
In the given figure, ABC is a triangle in which ∠ABC < 90° and AD ⊥ BC. Prove that AC2 = AB2 + BC2 − 2BC.BD.

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.
Find the length diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.
In ∆ABC, ∠BAC = 90°, seg BL and seg CM are medians of ∆ABC. Then prove that:
4(BL2 + CM2) = 5 BC2

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 triangle ABC, AB = AC = x, BC = 10 cm and the area of the triangle is 60 cm2.
Find x.
In a rectangle ABCD,
prove that: AC2 + BD2 = AB2 + BC2 + CD2 + DA2.
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
Show that the triangle ABC is a right-angled triangle; if: AB = 9 cm, BC = 40 cm and AC = 41 cm
Find the Pythagorean triplet from among the following set of numbers.
2, 4, 5
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`
A man goes 18 m due east and then 24 m due north. Find the distance of his current position from the starting point?
If S is a point on side PQ of a ΔPQR such that PS = QS = RS, then ______.
In the adjoining figure, a tangent is drawn to a circle of radius 4 cm and centre C, at the point S. Find the length of the tangent ST, if CT = 10 cm.

Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is ______.
The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground then the actual height of the tree is ______.
