Question

length and breadth of a rectangle are in ratio 4:3 if the diagonal is 25 cm then perimeter

Answer 1

Heya user
Here is your answer !!

length and breadth of a rectangle are in ratio 4:3 .

So , let the length be 4x and the breadth be 3x.

Formula of a diagonal = √(l²+b²)
Diagonal = 25 cm

So , ATQ ,
√{(4x)² + (3x)²} = 25
=> {(4x)² + (3x)²} = 625
=> 16x² + 9x² = 625
=> 25x² = 625
=> x² = 25
=> x = 5 .

So , the length of the rectangle is 20 cm and the breadth of the rectangle is 15 cm .

Hence , perimeter = 2(l+b)
= 2(20+15) cm
= 2*35 cm
= 70 cm (Ans)

Hope it helps !!

Answer 2

$\huge{\underline{\underline{\bf{Solution}}}}$

$\rule{200}{2}$

$\tt Given\begin{cases} \sf{Ratio \: of \: Length\: and \: breadth = 4:3} \\ \sf{Diagonal \: of \: rectangle = 25 \: cm} \end{cases}$

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to find the perimeter of rectangle.

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{Explanation :}}}}$

Let length of rectangle be 4x

So, Breadth of rectangle = 3x

We know that,

$\Large{\star{\boxed{\sf{Diagonal = \sqrt{(Length)^2 + (Breadth)^2}}}}}$

______________[Put Values]

$\sf{→Diagonal = \sqrt{(4x)^2 + (3x)^2}} \\ \\ \sf{→ 25 = \sqrt{16x^2 + 9x^2}} \\ \\ \sf{→ 25 = \sqrt{25x^2}} \\ \\ \sf{→ 25 = 5x} \\ \\ \sf{→x = \frac{\cancel{25}}{\cancel{5}}} \\ \\ \sf{→x = 5}$

Length (L) = 4x = 4(5) = 20 cm

Breadth (B) = 3x = 3(5) = 15 cm

$\rule{200}{2}$

Now,

$\Large{\star{\boxed{\rm{Perimeter = 2(L + B)}}}}$

$\sf{→ Perimeter = 2(20 + 15)} \\ \\ \sf{→Perimeter = 2(35)} \\ \\ \sf{→Perimeter = 70} \\ \\ \sf{\therefore \: Perimeter \: of \: rectangle \: is \: 70 \: cm.}$