from a handpicked tutor in LIVE 1-to-1 classes

# ABCD is a quadrilateral. Is AB + BC + CD + DA > AC + BD?

**Solution:**

This question is based on the triangle inequality theorem that the sum of lengths of two sides of a triangle is always greater than the third side.

Now visually identify that the quadrilateral ABCD. It is divided by diagonals AC and BD into four triangles.

Now, take each triangle separately and apply the above property and then add L.H.S and R.H.S of the equation formed.

In triangle ABC,

AB + BC > AC ……………(1)

In triangle ADC,

AD + CD > AC ………….. (2)

In triangle ADB,

AD + AB > DB --------------(3)

In triangle DCB,

DC+ CB > DB..................(4)

Adding equation (1), (2), (3) and (4) we get,

AB + BC + AD + CD + AD + AB + DC+ CB > AC + AC + DB + DB

AB + AB + BC + BC + CD + CD + AD + AD > 2AC + 2DB

2AB + 2BC + 2CD + 2AD > 2AC + 2DB

AB + BC + CD + AD > AC + DB

Hence, AB + BC + CD + DA > AC + BD is true

Useful Tip:

Whenever you encounter problems of this kind, it is best to think of the property based on the sum of lengths of any two sides of a triangle is always greater than the third side.

**☛ Check: **NCERT Solutions for Class 7 Maths Chapter 6

**Video Solution:**

## ABCD is a quadrilateral. Is AB + BC + CD + DA > AC + BD?

NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.4 Question 4

**Summary:**

ABCD is a quadrilateral. Hence AB + BC + CD + DA > AC + BD is true.

**☛ Related Questions:**

- Is It Possible To Have A Triangle With The Following Sides I 2 Cm 3 Cm 5 Cm Ii 3 Cm 6 Cm 7 Cm Iii 6 Cm 3 Cm 2 Cm
- Take Any Point O In The Interior Of A Triangle Pqr Is I Op Oq Pq Ii Oq Or Qr Iii Or Op Rp
- Am Is A Median Of A Triangle Abc Is Ab Bc Ca 2 Am Consider The Sides Of Triangles Abm And Amc
- The Lengths Of Two Sides Of A Triangle Are 12 Cm And 15 Cm Between What Two Measures Should The Length Of The Third Side Fall

visual curriculum