Question

any one can answer me plz I want to study for my exam .my teacher having health promblem so she can't answer any intelligent in brainly plz answer plz ​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• ABCD is a square of side x cm

• EFGH is a square of side y cm

Further given that,

• Sum of all sides = 52 cm

It means

• Perimeter of square ABCD + Perimeter of square EFGH is 52 cm

We know,

$\purple{\rm :\longmapsto\:\boxed{\tt{ Perimeter_{[square]} \: = \: 4 \times side \: }}}$

So, using this, we have

$\rm :\longmapsto\:4x + 4y = 52$

$\rm :\longmapsto\:4(x + y) = 52$

$\rm\implies \:\boxed{\tt{ x + y = 13}} - - - - (1)$

Now, Further given that,

• If square EFGH is cutting out from square ABCD, the area of remaining part is 91 square cm.

It means

$\rm :\longmapsto\:Area_{[ABCD]} - Area_{[EFGH]} = 91$

We know,

$\purple{\rm :\longmapsto\:\boxed{\tt{ Area_{[square]} = 4 \times side}}}$

So, using this, we get

$\rm :\longmapsto\: {x}^{2} - {y}^{2} = 91$

can be further rewritten as using algebraic Identity,

$\rm :\longmapsto\:(x + y)(x - y) = 91$

$\rm :\longmapsto\:13(x - y) = 91$

$\red{ \bigg\{  \sf \: \because \: using \: equation \: (1) \bigg\}}$

$\rm\implies \:\boxed{\tt{ x - y = 7}} - - - - (2)$

On adding equation (1) and (2), we get

$\rm :\longmapsto\:2x = 13 + 7$

$\rm :\longmapsto\:2x = 20$

$\rm\implies \:\boxed{ \: \bf \: \: x \: = \: 10 \:cm \: \: }$

On substituting the value of x in equation (1), we have

$\rm :\longmapsto\:10 + y = 13$

$\rm :\longmapsto\:y = 13 - 10$

$\rm\implies \:\boxed{ \: \bf \: \: y \: = \: 3 \:cm \: \: }$

So,

$\rm\implies \:\boxed{Side_{[square \: EFGH]} = y \: = 3 \: cm}$

and

$\rm\implies \:\boxed{Side_{[square \: ABCD]} = x \: = 10 \: cm}$

Also,

$\rm :\longmapsto\:\boxed{Area_{[square \: ABCD]} = {10}^{2} = 100 \: {cm}^{2} }$

$\rm :\longmapsto\:\boxed{Area_{[squareEFGH] }\: = {3}^{2} = 9 \: {cm}^{2} }$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$