Advertisements
Advertisements
Question
Which of the following can be the sides of a right triangle?
1.5 cm, 2 cm, 2.5 cm
In the case of right-angled triangles, identify the right angles.
Advertisements
Solution
1.5 cm, 2 cm, 2.5 cm
(1.5)2 = 2.25
(2)2 = 4
(2.5)2 = 6.25
Here,
2.25 + 4 = 6.25
(1.5)2 + (2)2 = (2.5)2
The square of the length of one side is the sum of the squares of the lengths of the remaining two sides. Hence, these are the sides of a right-angled triangle.
Right angle will be in front of the side of measure 2.5 cm.
APPEARS IN
RELATED QUESTIONS
In Fig., ∆ABC is an obtuse triangle, obtuse angled at B. If AD ⊥ CB, prove that AC2 = AB2 + BC2 + 2BC × BD
In figure, ∠B of ∆ABC is an acute angle and AD ⊥ BC, prove that AC2 = AB2 + BC2 – 2BC × BD
In the following figure, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that
(i) OA2 + OB2 + OC2 − OD2 − OE2 − OF2 = AF2 + BD2 + CE2
(ii) AF2 + BD2 + CE2 = AE2 + CD2 + BF2
A man goes 40 m due north and then 50 m due west. Find his distance from the starting point.
In a rectangle ABCD,
prove that: AC2 + BD2 = AB2 + BC2 + CD2 + DA2.
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.
Each side of rhombus is 10cm. If one of its diagonals is 16cm, find the length of the other diagonals.
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 - AB2 = 2BC x ED
If S is a point on side PQ of a ΔPQR such that PS = QS = RS, then ______.
In an isosceles triangle PQR, the length of equal sides PQ and PR is 13 cm and base QR is 10 cm. Find the length of perpendicular bisector drawn from vertex P to side QR.
