Question

The length and breadth of a rectangle are in the ratio 4 ratio 3 if the diagonal measure 25 CM then the perimeter of a rectangle is?

Answer 1

let length be 4x  

so breadth= 3x  

hence by Pythagorian Rule  

Diagonal=hypotenuse == [4x]^2 +[3x]^2= [5]^2  

16x^2 +9x^2= 6 25  

25x^2 =625  

x=25`  

hence length=4 x25cm=100cm  

breadth= 3x 25cm = 75cm  

thus perimeter=P= 2[length+ breadth]= 2[100+75]cm  

P== 350cm

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,

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

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