Home
Class 9
MATHS
In trapezium ABCD, AB//DC. M is mid poin...

In trapezium ABCD, AB//DC. M is mid point of AD and N is mid-point of BC.
If AB = 5.7 cm and MN = 6.2 cm , find DC.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the length of side DC in trapezium ABCD where AB is parallel to DC, and M and N are the midpoints of sides AD and BC, respectively. ### Step-by-Step Solution: 1. **Identify the Given Information:** - AB = 5.7 cm - MN = 6.2 cm - M is the midpoint of AD. - N is the midpoint of BC. 2. **Use the Midsegment Theorem:** The length of the segment connecting the midpoints of the non-parallel sides (MN) in a trapezium is given by the formula: \[ MN = \frac{AB + DC}{2} \] Here, we need to find DC. 3. **Set Up the Equation:** From the Midsegment Theorem, we can write: \[ 6.2 = \frac{5.7 + DC}{2} \] 4. **Multiply Both Sides by 2:** To eliminate the fraction, multiply both sides by 2: \[ 2 \times 6.2 = 5.7 + DC \] \[ 12.4 = 5.7 + DC \] 5. **Isolate DC:** Now, we can isolate DC by subtracting 5.7 from both sides: \[ DC = 12.4 - 5.7 \] 6. **Calculate DC:** Perform the subtraction: \[ DC = 6.7 \text{ cm} \] ### Final Answer: DC = 6.7 cm
Promotional Banner

Topper's Solved these Questions

  • CHAPTERWISE REVISION (STAGE 1)

    ICSE|Exercise pythagoras therorem|9 Videos

  • CHAPTERWISE REVISION (STAGE 1)

    ICSE|Exercise Rectillinear figures|24 Videos

  • CHAPTERWISE REVISION (STAGE 1)

    ICSE|Exercise Inequalities|5 Videos

  • CHAPTER REVISION (STAGE 2)

    ICSE|Exercise DISTANCE FORMULA |12 Videos

  • CHAPTERWISE REVISION (STAGE 3)

    ICSE|Exercise DISTANCE FORMULA |11 Videos

Similar Questions

Explore conceptually related problems

In trapezium ABCD, AB//DC. M is mid point of AD and N is mid-point of BC. If AB = 8 cm and DC = 11 cm , find MN.

In triangle ABC, P is mid-point of AB and Q is mid-point of AC. If AB = 9.6 cm, BC = 11 cm and AC = 11.2 , find the perimeter of the trapezium PBCQ.

If in triangleABC , AD is the bisector of angleA and D lies on BC. If AB = 6.4 cm, AC = 8 cm, BD = 5.6 cm, find DC.

In the figure , given below. ABCD is a trapezium in which AB /DC , P is mid- point of AD and Q is mid-point of Bc. Write a relations connecting AB , PQ and DC. (ii) Find DC. If AB = 16 cm and PQ = 23 cm

In the adjoining figure (i) AB=BC, M is the mid -point of AB and N is the mid- point of BC. Show that AM=NC. (ii) BM=BN,M is the mid- point of AB and N is the mid - point of BC. Show that AB=BC.

In trapezium ABCD, sides AB and DC are parallel to each other. E is mid-point of AD and F is mid-point of BC. Prove that : AB + DC = 2EF.

In the given figure, M is mid-point of AB and DE, whereas N is mid-point of BC and DF. Show that : EF = AC.

In the adjoining figure, DeltaABC is right angled at C and M is the mid-point of hypotenuse AB, If AC = 32 cm and BC = 60 cm, then find the length of CM.

In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.

In a trapezium ABCD, AB/DC, E is mid-point of aD. A line through E and parallel to AB intersects BC at point F. Show that: 2EF=AB+DC