Math, asked by Anonymous, 10 months ago

adjacent side of a parallelogram are in the ratio 3 ratio 8 and the perimeter is is 110 find the sides of parallelogram​

Answers

Answered by Anonymous
16

Given:

  • Adjacent sides of a paralleogram are in ratio 3:8.
  • Perimeter of paralleogram is 110 units .

To Find:

  • The measure of sides of the paralleogram.

Answer:

Given that adjacent sides are in ratio 3:8.

Let us take the ratio be 3x:8x .

Some points about paralleogram:

  1. ☞Opposite sides are equal .
  2. ☞Opposite angles are equal.
  3. ☞Adjacent angles sum is 180°.
  4. ☞Diagonals bisect each other.

From properties of paralleogram its clear that the other two sides will be 3x and 8x .

{\boxed{\purple{\sf{Perimeter = Sum\: of \:all \:sides }}}}

=> Perimeter = 3x+3x+8x+8x .

=> Perimeter = 6x + 16x .

{\underline{\boxed{\red{\sf{\leadsto Perimeter= 22x}}}}}

But it is given 110 units. So ,

\sf{\implies 22x=110u}

\sf{\implies x=\dfrac{110u}{22}}

{\underline{\boxed{\red{\sf{\leadsto x=5u}}}}}

Hence

  • ☞Measure of first side = 3x = 3×5u=15 units.
  • ☞Measure of second side = 8x=8×5u = 40 units.
  • ☞Measure of third side = 3x = 3×5u=15units.
  • ☞Measure of fourth side = 8x =8×5u = 40 units.
Attachments:
Answered by prince5132
10

GIVEN :-

  • Adjacent sides of parallelogram are in the ratio 3:8

  • Perimeter of Parallelogram is 110 unit

TO FIND :-

  • The sides of parallelogram = ?

SOLUTION :-

\setlength{ \unitlength}{20} \begin{picture}(3,5) \put(2,2){ \line(1,0){4}}\put(2,2){ \line(1,1){3}}\put(6,2){ \line(1,1){3}}   \put(5,5){ \line(1,0){4}}  \put(2,1.5 ){$ \tt A$ } \put(6, 1.5){$ \tt B $ } \put(5,5.2){$ \tt D $ } \put(9.3, 5){$ \tt C$ } \put(4, 1.5){$ \tt 8x $ } \put(7.5,3 ){$ \tt 3x $ } \put(3, 3.5){$ \tt 3x $ } \put(7,5.2 ){$ \tt 8x $ } \\ \put(8,1){\framebox{$ \tt @prince5132 $}}\end{picture}

Let, the ratio constant be x

Therefore, Adjacent sides be = 3x and 8x

▪︎perimeter of parallelogram = 110 unit

=> 2 (3x + 8x) = 110

=> 2 (11x) = 110

=> 22x = 110

=> x = 110/22

=> x = 5

Hence,

▪︎Side ,AD = 3x = 3 × 5 = 15 unit

AB = 8x = 8 × 5 = 40 unit

BC = 3x = 3 × 5 = 15 unit

CD = 8x = 8 × 5 = 40 unit

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