Question

find the perimeter of a rectangle whose length is 5a + 6b and breadth is 4a - b​

Answer 1

ANSWER

l=6cm,       b=4cm

Area of rectangle =l×b=6×4=24cm2

Area of Δ=21×b×h=3×area of rectangle

1××h=×24

             h=24cm

Answer 2

Given :

• Length of the Rectangle = (5a + 6b)

• Breadth of the Rectangle = (4a - b)

To find :

The perimeter of the Rectangle

Solution :

We know the formula for perimeter of a Rectangle i.e,

$\boxed{\bf{Perimeter = 2(Length + Breadth)}}$

Now using the above formula and substituting the values in it , we get :

$:\implies \bf{P = 2[(5a + 6b) + (4a - b)]}$

$:\implies \bf{P = 2(5a + 6b + 4a - b)}$

$:\implies \bf{P = 10a + 12b + 8a - 2b)}$

$:\implies \bf{P = 18a + 10b}$

$\boxed{\therefore \bf{P = 18a + 10b}}$

Hence, the perimeter of the Rectangle is 18a + 10b.

Additional Information :

Area of the Rectangle :

Given :

• Length of the Rectangle = (5a + 6b)

• Breadth of the Rectangle = (4a - b)

To find :

The area of the Rectangle :

Solution :

We know the formula for area of a Rectangle i.e

$\boxed{\bf{Area = Length \times Breadth}}$

Now using the above formula and substituting the values in it, we get :

$:\implies \bf{Area = Length \times Breadth}$

$:\implies \bf{A = (5a + 6b) \times (4a - b)}$

$:\implies \bf{A = 5a(4a - b) + 6b(4a - b)}$

$:\implies \bf{A = 20a^{2} - 5ab + 24ab - 6b^{2}}$

$:\implies \bf{A = 20a^{2} + 19ab - 6b^{2}}$

$\boxed{\therefore \bf{A = 20a^{2} + 19ab - 6b^{2}}}$

Hence, the area of the Rectangle is 20a² + 19ab - 6b².