Question

If a side of a parallelogram is two-third of its adjacent side and the sum of all the sides is 14 cm then what is the difference between its adjacent sides?
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Answer 1

Answer:

1.4 cm

Step-by-step explanation:

As per the provided information in the given question, we have :

• A side of a parallelogram is two-third of its adjacent side.
• Sum of all the sides is 14 cm.

We've been asked to calculate the difference between its adjacent sides.

Let us suppose one side (AB) be x cm. Thus, side adjacent to it is (BC) that becomes ⅔x cm.

Now, it is known to us that opposite sides of a parallelogram are equal. Thus,

• AB = x cm
• BC = ⅔x cm
• CD = x cm
• DA = ⅔x cm

Now, according to the question, the sum of all the sides is 14 cm. That implies,

$\longrightarrow \sf{\quad {AB + BC + CD + DA = 14 \; cm }}$

Substitute the values of sides.

$\longrightarrow \sf{\quad { \Bigg \lgroup x + \dfrac{2}{3}x + x + \dfrac{2}{3}x \Bigg \rgroup \; cm= 14 \; cm }}$

Taking the LCM in L.H.S and performing addition.

$\longrightarrow \sf{\quad { \Bigg \lgroup \dfrac{3x + 2x + 3x + 2x}{3} \Bigg \rgroup \; cm= 14 \; cm }}$

Performing addition in the numerator of the fraction in LHS.

$\longrightarrow \sf{\quad { \Bigg \lgroup \dfrac{10x}{3} \Bigg \rgroup \; cm= 14 \; cm }}$

Transposing 3 from LHS to RHS. Its arithmetic operator will get changed.

$\longrightarrow \sf{\quad { 10x \; cm= 14 \times 3 \; cm }}$

Performing multiplication in RHS.

$\longrightarrow \sf{\quad { 10x \; cm= 42 \; cm }}$

Transposing 10 from LHS to RHS. Its arithmetic operator will get changed.

$\longrightarrow \sf{\quad { x \; cm= \cancel{\dfrac{42}{10}} \; cm }}$

Dividing 42 by 10.

$\longrightarrow \quad\boxed{\sf { x \; cm= 4.2 \; cm }}$

Therefore, measure of AB and CD is 4.2 cm.

Now,

$\longrightarrow \sf{\quad {BC \; \& \; DA = \dfrac{2}{3}x \; cm }}$

Substitute the value of x.

$\longrightarrow \sf{\quad {BC \; \& \; DA = \dfrac{2}{3}(4.2) \; cm }}$

Performing multiplication in RHS.

$\longrightarrow \sf{\quad {BC \; \& \; DA = \cancel{\dfrac{8.4}{3}} \; cm }}$

Cancelling the terms.

$\longrightarrow \quad\boxed{\sf {BC \; \& \; DA = 2.8 \; cm }}$

Therefore, the measure of BC and DA is 2.8 cm.

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

In the question, we've been asked to calculate the difference between its adjacent sides. Let us denote the difference by D. Thus,

$\longrightarrow \sf{\quad { D = \Big \{4.2 - 2.8 \Big \} \; cm }}$

Performing subtraction.

$\longrightarrow \quad \underline{\boxed {\textbf{\textsf{ D = 1.4 \; cm}} }}$

Therefore, the difference between its adjacent sides is 1.4 cm.