Question

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

Answer 1

(diagonals of rectangle are equal).)
let the length and breadth be x.so,l=4x &b=3x.
now,by pythagorus theorem,
length^2+breadth^2=diagonal^2.
(4x)^2+(3x)^2=25^2.
16x^2+9x^2=625.
25x^2=625
x^2=25
so,value of x=5.
now,peimeter of rectangle=2(l+b)=2(4*5+3*5)=2(35)=70cm

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,

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

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