Home/Class 7/Maths/

Question and Answer

\(ABCD\) is quadrilateral. Is \(AB + BC + CD + DA < 2 (AC + BD)\)
loading
settings
Speed
00:00
04:07
fullscreen

Question
MathsClass 7

\(ABCD\) is quadrilateral. Is \(AB + BC + CD + DA < 2 (AC + BD)\)

Answer

Yes
To Keep Reading This Answer, Download the App
4.6
star pngstar pngstar pngstar pngstar png
Review from Google Play
To Keep Reading This Answer, Download the App
4.6
star pngstar pngstar pngstar pngstar png
Review from Google Play

Solution

Let us consider \(ABCD\) is quadrilateral and \(P\) is the point where the diagonals are intersect. As shown in the figure below.
Solution for ABCD is quadrilateral. Is AB + BC + CD + DA < 2 (AC + BD)
We know that,
The sum of the length of any two sides is always greater than the third side.
Now consider the \(ΔPAB\),
Here, \(PA+PB>AB\) … [equation i]
Then, consider the \(ΔPBC\)
Here, \(PB+PC>BC\) … [equation ii]
Consider the \(ΔPCD\)
Here, \(PC+PD>CD\) … [equation iii]
Consider the \(ΔPDA\)
Here, \(PD+PA>DA\) … [equation iv]
By adding equation [i], [ii], [iii] and [iv], we get,\(PA+PB+PB+PC+PC+PD+PD+PA>AB+BC+CD+DA\)
\(\implies 2PA+2PB+2PC+2PD>AB+BC+CD+DA\)
\(\implies 2PA+2PC+2PB+2PD>AB+BC+CD+DA\)
\(\implies 2(PA+PC)+2(PB+PD)>AB+BC+CD+DA\)
From the figure we have, \(AC = PA + PC\) and \(BD = PB + PD\)
Then,
\(2AC+2BD>AB+BC+CD+DA\)
\(\implies 2(AC+BD)>AB+BC+CD+DA\)
Hence, the given expression is true.
To Keep Reading This Solution, Download the APP
4.6
star pngstar pngstar pngstar pngstar png
Review from Google Play
To Keep Reading This Solution, Download the APP
4.6
star pngstar pngstar pngstar pngstar png
Review from Google Play
Correct58
Incorrect0
Still Have Question?
Ask Your QuestionFind More Answer
Watch More Related Solutions
Find the square roots of \(100\) and \(169\) by the method of repeated subtraction.
Find the square roots of \(100\) and \(169\) by the method of repeated subtraction.
Math|Class 8
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as \(2, –7, –14\) respectively. 
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as \(2, –7, –14\) respectively. 
Math|Class 10
If \(60\)% people in city like cricket, \(30\)% like football and the remaining like other games, then what per cent of the people like other games? If the total number of people are \(50\) lakh, find the exact number who like each type of game.
If \(60\)% people in city like cricket, \(30\)% like football and the remaining like other games, then what per cent of the people like other games? If the total number of people are \(50\) lakh, find the exact number who like each type of game.
Math|Class 8
Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.
\((p,q);(10m,5n);(20{x}^{2},5{y}^{2});(4x,3{x}^{2});(3mn,4np)\)
Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.
\((p,q);(10m,5n);(20{x}^{2},5{y}^{2});(4x,3{x}^{2});(3mn,4np)\)
Math|Class 8
Evaluate:\( (-36)\div (-9)\)
Evaluate:\( (-36)\div (-9)\)
Math|Class 7
A contractor plans to install two slides for the children to play in a park. For the children below the age of \(5\) years, she prefers to have a slide whose top is at a height of \(1.5\ m\), and is inclined at an angle of \(30^o\) to the ground, whereas for elder children, she wants to have a steep slide at a height of \(3\ m\), and inclined at an angle of \(60^o\) to the ground. What should be the length of the slide in each case?
A contractor plans to install two slides for the children to play in a park. For the children below the age of \(5\) years, she prefers to have a slide whose top is at a height of \(1.5\ m\), and is inclined at an angle of \(30^o\) to the ground, whereas for elder children, she wants to have a steep slide at a height of \(3\ m\), and inclined at an angle of \(60^o\) to the ground. What should be the length of the slide in each case?
Math|Class 10
A farmer has enough food to feed \(20\) animals in his cattle for \(6\) days. How long would the food last if there were \(10\) more animals in his cattle?
A farmer has enough food to feed \(20\) animals in his cattle for \(6\) days. How long would the food last if there were \(10\) more animals in his cattle?
Math|Class 8
An umbrella has \(8\) ribs which are equally spaced. Assuming umbrella to be a flat circle of radius \(45\ cm\), find the area between the two consecutive ribs of the umbrella.
An umbrella has \(8\) ribs which are equally spaced. Assuming umbrella to be a flat circle of radius \(45\ cm\), find the area between the two consecutive ribs of the umbrella.
Math|Class 10
Find the area of the shaded region in Fig, if \(ABCD\) is a square of side \(14 cm\) and \(APD\) and \(BPC\) are semicircles.
Find the area of the shaded region in Fig, if \(ABCD\) is a square of side \(14 cm\) and \(APD\) and \(BPC\) are semicircles.
Math|Class 10
If \(21y5\) is a multiple of \(9\), where \(y\) is a digit, what is the value of \(y\)?
If \(21y5\) is a multiple of \(9\), where \(y\) is a digit, what is the value of \(y\)?
Math|Class 8

Load More

More Solution Recommended For You
NCERT Maths for Class 6
NCERT Physics for Class 6
NCERT Chemistry for Class 6
NCERT Biology for Class 6
NCERT Maths for Class 7
NCERT Physics for Class 7
NCERT Chemistry for Class 7
NCERT Biology for Class 7
NCERT Maths for Class 8
NCERT Physics for Class 8
NCERT Chemistry for Class 8
NCERT Biology for Class 8
Previous
Next