A quadrilateral has distinct integer side lengths. If the second largest side has length 10, then find the maximum possible length of the largest side.
A.25
B.26
C.27
D.28
Last updated date: 28th Mar 2023
•
Total views: 308.7k
•
Views today: 3.85k
Answer
308.7k+ views
Hint: We are going to solve the given problem by using the idea that in a quadrilateral, the largest side length should be less than the sum of lengths of the remaining three sides.
Let ‘a’ the largest side, ‘b’ be the second largest side, ‘c’ be the third largest side and ‘d’ be the smallest side of the given quadrilateral.
$ \Rightarrow $a > b > c > d
Given that the length of the second largest side b = 10.
Then the largest possible values for d and c are 8 and 9 respectively.
By the triangle inequality,
$$\eqalign{
& a < b + c + d \cr
& \Rightarrow a < 10 + 9 + 8 \cr
& \Rightarrow a < 27 \cr} $$
The maximum value that ‘a’ can take is 26.
$\therefore $The maximum possible length of the given quadrilateral is 26.
Note:
Triangular inequality states that the sum of any two sides of a triangle must be greater than the measure of the third side. In the same way it is applicable to quadrilaterals.
Let ‘a’ the largest side, ‘b’ be the second largest side, ‘c’ be the third largest side and ‘d’ be the smallest side of the given quadrilateral.
$ \Rightarrow $a > b > c > d
Given that the length of the second largest side b = 10.
Then the largest possible values for d and c are 8 and 9 respectively.
By the triangle inequality,
$$\eqalign{
& a < b + c + d \cr
& \Rightarrow a < 10 + 9 + 8 \cr
& \Rightarrow a < 27 \cr} $$
The maximum value that ‘a’ can take is 26.
$\therefore $The maximum possible length of the given quadrilateral is 26.
Note:
Triangular inequality states that the sum of any two sides of a triangle must be greater than the measure of the third side. In the same way it is applicable to quadrilaterals.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
