Question

The adjacent sides of a parallelogram are in the ratio 4:5. Find the longer side if the perimeter is 90cm.​

Answer 1

Given :

• Ratio of Adjacent Sides = 4:5
• Perimeter of Parallelogram = 90 cm

To Find :

• Find the Longer Side

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

$\dag$ Formula Used :

$\qquad {\purple{\bigstar \; \; {\pink{\underbrace{\underline{\red{\sf{ Perimeter {\small_{(Parallelogram)}} = 2 \bigg( a + b \bigg) }}}}}}}}$

Where :

• a = First Adjacent Side
• b = Second Adjacent Side

$\dag$ Let the Ratios :

• a = 4y
• b = 5y

$\dag$ Calculating the Value of y :

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { Perimeter = 2 \bigg( a + b \bigg) } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { 90 = 2 \bigg( 4y + 5y \bigg) } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { 90 = 2 \times 9y } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { 90 = 18y } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { \dfrac{90}{18} = y } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; \sf { \cancel\dfrac{90}{18} = y } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\frak { y = 5 }}}}} \; {\orange{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\dag$ Calculating the Adjacent Sides :

• a = 4y = 4(5) = 20 cm
• b = 5y = 5(5) = 25 cm

$\therefore \;$ The longer Adjacent Side is 25 cm .

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Answer 2

Answer:

✰Given:-

• ✯ The adjacent sides of a parallelogram are in the ratio 4 : 5.
• ✯ Perimeter of the parallelogram = 90cm.

✰Formula used:-

Perimeter of a parallelogram = 2( a + b ).

where,

• ꙳ a = 4x.
• ꙳ b = 5x.
• ꙳ Perimeter = 90cm.

✰Solution:-

Let, the ratio of the adjacent sides be 4x and 5x.

Now,

Perimeter = 2( a + b ).

90 = 2( 4x + 5x ).

90 = 2(9x).

90 = 18x.

x = 90/18.

• x = 5.

Hence,

• ✯ Length of first adjacent side (a) = 4x = 4 × 5 = 20cm.
• ✯ Length of second adjacent side (b) = 5x = 5 × 5 = 25cm.