Question

THE LENGTH AND BREADTH OF A RRCTANGLE ARE IN RATIO 4:3 AND THE DIAGONAL MEASURES 10 CM THEN ITS PERIMETER IS

Answer 1

Answer:

P = 28 cm

Step-by-step explanation:

the diagonal divides the rectangle into 2 right triangles with the diagonal as hypotenuse.

the ratio of length : breadth = 4 : 3 = 4x : 3x ( x is a multiplier )

using Pythagoras' identity in the right triangle

(4x)² + (3x)² = 10²

16x² + 9x² = 100

25x² = 100 ( divide both sides by 25 )

x² = 4 ( take square root of both sides )

x = $\sqrt{4}$ = 2

then

length = 4x = 4 × 2 = 8 cm

breadth = 3x = 3 × 2 = 6 cm

perimeter (P) is calculated as

P = 2 × length + 2 × breadth

  = 2 × 8 + 2 × 6

  = 16 + 12

  = 28 cm

Answer 2

Answer:

perimeter = 28 cm

Step-by-step explanation:

$\frac{L}{w} =\frac{4}{3}$

Then

$L = \frac{4}{3} w$

By applying the Pythagorean theorem:

L² + w² = 10²

Then

$\left( \frac{4}{3} w\right)^{2} +w^{2}=100$

Then

$\frac{16}{9} w^{2} +w^{2}=100$

Then

$\frac{25}{9} w^{2}=100$

Then

$w^2=\frac{9\times100}{25} =\frac{900}{25}$

Then

w = 30/5

   = 6

Then

$L = \frac{4}{3} \times6 = \frac{24}{3} =8$

Perimeter = 2×(L + w)

                = 2×(8 + 6)

                = 2×(14)

                = 28