Question

the length and breadth of a rectangle are in the ratio 4:3 and diagonal is equal to 25cm . fid length and breadth​

Answer 1

Answer:

Let x be the common multiple.

Length = 4x

Breadth = 3x

According to Pythagoras theorem,

(4x)²+(3x)²=(25)²

16x²+9x²=625

25x²=625

x²=625/25

X =5

So,

Length = 4x = 20 cm

Breadth = 3x = 15 cm

Perimeter = 2(l×b)

= 2 (20 + 15)

= 70 cm

So, perimeter of rectangle is 70 cm.

Answer 2

$\begin{gathered}\large {\boxed{\sf{\mid{\overline {\underline {\star ANSWER ::}}}\mid}}}\end{gathered}$

Given :-

• Ratio of length and breadth of a rectangle = 4:3
• Diagonal = 25 cm

To Find :-

• Length and Breadth

Solution :-

Let the length and breadth of the rectangle be 4x and 3x as the given ratio is 4:3.

And the diagonal is given as 25cm.

We know that, In a rectangle,

$\boxed {\sf \: { {diagonal}^{2} = {length}^{2} + {breadth}^{2} }}$

So, substituting the values,

$\sf {{25}^{2} = {(4x)}^{2} + {(3x)}^{2} } \\ \sf{625 = 16 {x}^{2} + 9 {x}^{2} } \\ \sf{625 = 25 {x}^{2} } \\ \sf{25 = {x}^{2} } \\ \sf{x = \sqrt{25} } \\ \sf{x = 5}$

Therefore, length and breadth can be found as :

• Length = 4x = 4(5) = 20 cm
• Breadth = 3x = 3(5) = 15 cm

@SweetestBitter