Question

Q. In figure ABCD is
a rectangle. Find
the values of x and y.​

Answer 1

Step-by-step explanation:

see the attachment

hope it works

Answer 2

$\large \bf {\color{blue}{\diamond \: \: Question:-}}$

In figure, ABCD is a rectangle. Find the values of x and y.

$\large \bf \color{blue}{\diamond \: \: Solution:-}$

As opposite sides are equal in a rectangle,

• AB = DC (x+y=30cm)....(1)
• AD = BC (x-y=14cm)....(2)

Since eq. (1) and (2) are a pair of linear equations in two variables, we'll solve them by substitution method :-

${\color{red}\implies} \sf x + y = 30$

${\color{red}\implies}\sf x=30-y....(3)$

Substituting eq. (3) in eq. (2) and solving :-

${\color{red}\implies}\sf x - y = 14$

${\color{red}\implies}\sf (30-y)-y=14$

${\color{red}\implies}\sf 30-2y=14$

${\color{red}\implies}\sf -2y=14-30$

${\color{red}\implies}\sf -2y=-16$

${\color{red}\implies}\sf y= \cancel\cfrac{-16}{-2}$

$\boxed {\color{teal}\therefore~ \bf y=8}$

Substituting y=8 in eq. (3) :-

${\color{red}\implies}\sf x=30-y$

${\color{red}\implies}\sf x=30-8$

$\boxed {{\color {teal}\therefore~\bf x=22}}$

$\large \bf {\color{blue} \diamond \: \: Verification:-}$

Now, substituting x=22 and y=8 in DC and BC :-

${\color{red}\implies}\sf DC \: : \: x+y = 30m$

${\color{red}\implies}\sf DC \: : \: 22+8=30cm$

${\color{red}\implies}\sf 30cm=30cm$

$\boxed{\bf \color{teal}\therefore \: AB= DC}$

${\color{red}\implies}\sf BC \: : \: x - y = 14cm$

${\color{red}\implies}\sf BC \: : \: 22-8=14cm$

${\color{red}\implies}\sf 14cm=14cm$

$\boxed{\bf \color{teal}\therefore \: AC= BC}$

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Hope the explaination is clear!