Question

simultaneous equation​

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given a rectangle whose length is 5 cm more than 4 times it's breadth
• When length is reduced by 2 and breadth is increased by 2 the area of gets increased by 36

To Find:

• We have to find length and breadth of original rectangle

Concept Used:

This question can be solved using concept of linear equation in two variables which can be further solved using one of this technique

• Substitution
• Elimination
• Cross Multiplication

Solution:

Let Breadth of rectangle = y cm

Length of Rectangle = x cm

$\odot \:$According to first Condition :

Length is 5 cm more than 4 times it's breadth

$\boxed{\sf{Length = 4 \times Breadth + 5}}$

Substituting the Values

$\implies \boxed{\sf{x = 4y + 5}}$-------------------------(1)

$\sf{ }$

$\odot \:$According to second Condition

When length is reduced by 2 and breadth is increased by 2

• New length = x - 2
• New Breadth = y + 2

Area gets increased by 36

$\implies \sf{New \: area = xy + 36}$

$\implies \sf{Length \times Breadth = xy + 36}$

$\implies \sf{(x-2) \: (y+2) = xy + 36}$

$\implies \sf{xy + 2x - 2y - 4= xy + 36}$

$\implies \sf{\cancel{xy}+ 2x - 2y - 4 = \cancel{xy} + 36}$

$\implies \sf{2x - 2y = 36 + 4}$

$\implies \sf{2x - 2y = 40}$

$\implies \sf{x - y = 20}$

Putting value of x from Equation (1)

$\implies \sf{4y + 5 - y = 20}$

$\implies \sf{4y - y= 20 - 5}$

$\implies \sf{3y = 15}$

$\implies \sf{y = \dfrac{15}{3}}$

$\implies \boxed{\sf{y = 5 \: cm}}$

$\sf{ }$

$\odot \:$Finding Dimensions :

$\implies \sf{x = 4 \times 5 + 5}$

$\implies \sf{x = 20 + 5}$

$\implies \boxed{\sf{x = 25 \: cm}}$

_______________________________

$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

$\large\boxed{\sf{Length \: of \: Rectangle = 25 \: cm}}$

$\large\boxed{\sf{Breadth \: of \: Rectangle = 5 \: cm}}$

________________________________

$\huge\mathtt\green{Verification:}$

We have found the following values

• Length = 25 cm
• Breadth = 5 cm

Initially area = 25 x 5 = 125 cm²

When length is reduced by 2 and breadth is increased by 2 the area of gets increased by 36

• New length = 25 - 2 = 23 cm
• New breadth = 5 + 2 = 7 cm

Final area = 23 x 7 = 161 cm²

Area increased = Final - Initial

Area increased = 161 - 125

$\boxed{\sf{Area \: Increased = 36 \: cm^2}}$

$\large\red{\underline{\underline{\sf{Hence \: Verified \: !!! }}}}$