Question

The length and breadth of a rectangle are in the ratio 4:3 .If the diagonal measures 25 cm .Find the perimeter of rectangle

Answer 1

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your answer is - - - -

length=4x

breadth=3x

$a^2=b^2+c^2$

$25^2=(4x)^2+(3x)^2$

$625=16x^2+9x^2$

$625=25x^2$

$x^2=625/25$

$x^2=25$

$x=5$

$so,$

$length=4x= 4×5=20cm$

$breadth=3x=3×5=15cm$

$perimeter = 2 (l+b)$

$= 2 (20+15)$

$=2 (35)$

$=70cm2$

Answer 2

Given:

The length and breadth of a rectangle are in the ratio 4:3. The diagonal of the rectangle measures 25cm.

To Find:

The perimeter of the given rectangle.

Solution:

1. The length and breadth of the rectangle are in the ratio 4:3. Let the common factor of the length and the breadth be s, hence the length and the breadth of the rectangle are 4s, 3s respectively.

2. The length of the diagonal of the given rectangle is 25cm. The length of the diagonal of a rectangle is given by the formula,

=> Length of the diagonal =$\sqrt{length^{2}+breadth^{2} }$,

=> 25 = $\sqrt{(4s)^2+(3s)^2 }$,

=> 625 = 16s²+9s²,

=> 625 = 25s²,

=> s² = 25,

=> s = 5cm.

3. Therefore, the length and breadth of the rectangle will be,

=> Length = 4 x 5 = 20cm,

=> Breadth = 3 x 5 = 15cm.

4. The perimeter of the rectangle = 2 x (l + b),

=> Perimeter of the rectangle = 2 x (20 + 15),

=> Perimeter of the rectangle = 2 x 35,

=> Perimeter of the rectangle = 70cm.

Therefore, the perimeter of the rectangle is 70cm.