Advertisements
Advertisements
Question
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.
Advertisements
Solution
Yes, because in each case the sum of two sides is greater than the third side.
i.e., 7 + 4 > 8, 8 + 4 > 7, 7 + 8 > 4
Hence, it is possible to construct a triangle with given sides.
APPEARS IN
RELATED QUESTIONS
In Figure AB = AC and ∠ACD =105°, find ∠BAC.

In figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD
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 a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that LN = MN.
ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that ΔABC is isosceles
Which of the following statements are true (T) and which are false (F):
Angles opposite to equal sides of a triangle are equal
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)
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than twice the median drawn to the third side.
Fill in the blank to make the following statement true.
The sum of three altitudes of a triangle is ..... than its perimeter.
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.
Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =
If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?
In the given figure, the value of x is ______.

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.
Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that external angle adjacent to ∠ABC is equal to ∠BOC
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
