Advertisements
Advertisements
Question
Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be ______.
Options
3.6 cm
4.1 cm
3.8 cm
3.4 cm
Advertisements
Solution
Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be 3.4 cm.
Explanation:
Given, the length of two sides of a triangle are 5 cm and 1.5 cm, respectively.
Let sides AB = 5 cm and CA = 1.5 cm
We know that, a closed figure formed by three intersecting lines (or sides) is called a triangle, if difference of two sides < third side and sum of two sides > third side
∴ 5 – 1.5 < BC and 5 + 1.5 > BC
⇒ 3.5 < BC and 6.5 > BC
Here, we see that options (a), (b) and (c) satisfy the above inequality but option (d) does not satisfy the above inequality.
APPEARS IN
RELATED QUESTIONS
ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ABD = ∠ACD.
In Figure AB = AC and ∠ACD =105°, find ∠BAC.
Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.
In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15°
The vertical angle of an isosceles triangle is 100°. Find its base angles.
Find the measure of each exterior angle of an equilateral triangle.
ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles.
Which of the following statements are true (T) and which are false (F):
The measure of each angle of an equilateral triangle is 60°
Which of the following statements are true (T) and which are false (F):
The two altitudes corresponding to two equal sides of a triangle need not be equal.
O is any point in the interior of ΔABC. Prove that
(i) AB + AC > OB + OC
(ii) AB + BC + CA > OA + QB + OC
(iii) OA + OB + OC >` 1/2`(AB + BC + CA)
Fill in the blank to make the following statement true.
If two angles of a triangle are unequal, then the smaller angle has the........ side opposite to it.
ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Prove that ∠D = \[\frac{1}{2}\] ∠A.
Write the sum of the angles of an obtuse triangle.
In the given figure, for which value of x is l1 || l2?
The side BC of ΔABC is produced to a point D. The bisector of ∠A meets side BC in L. If ∠ABC = 30° and ∠ACD = 115°, then ∠ALC = ______.
D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC. Then ______.
In ∆PQR, if ∠R > ∠Q, then ______.
Is it possible to construct a triangle with lengths of its sides as 9 cm, 7 cm and 17 cm? Give reason for your answer.
Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.
In a triangle ABC, D is the mid-point of side AC such that BD = `1/2` AC. Show that ∠ABC is a right angle.
