Question

Find the value of 'a' and 'b' that would make the quadrilateral, a parallelogram.​

Answer 1

Question :-

Find the value of 'a' and 'b' that would make the quadrilateral, a parallelogram.

Solution :-

Learn a property

Property : Opposite side of Quadrilateral are same.

According to the property

♣ 5a - 13 = 3a - 5

♣ 8b = 10b - 3

Now,

$\sf:\longmapsto{5a - 13 = 3a - 5} \: \: \: \: \\ \\ \sf:\longmapsto{5 a - 3a = - 5 + 13 } \\ \\ \sf:\longmapsto{2a = 8} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf:\longmapsto{a = \cancel{ \frac{8}{2} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{a = 4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

And,

$\sf:\longmapsto{8b = 10b - 3} \\ \\ \sf:\longmapsto{10b - 8b = 3} \\ \\ \sf:\longmapsto{2b = - 3} \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{ \frac{ - 3}{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

The value of a is 4 and value of b is $\frac{ - 3}{2}$.

Verification :-

Replace the value a = 4

$\sf:\longmapsto{5(4) - 13 = 3(4) - 5} \\ \\ \sf:\longmapsto{20 - 13 = 12 - 5} \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{7 = 7} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Replace the value of b = $\frac{ - 3}{2}$

$\sf:\longmapsto{8 \bigg( \frac{ - 3}{2} \bigg) = 10 \bigg( \frac{ - 3}{2} \bigg) - 3 } \\ \\ \sf:\longmapsto{ \frac{ - 24}{2} = \frac{ - 30}{2} - 3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf:\longmapsto{ - 12 = - 15 - 3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{ - 12 = - 12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence Verified !

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