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

P = 28 cm

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 =
`√(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

perimeter = 28 cm

Explanation:

`(L)/(w) =(4)/(3)`

Then

`L = (4)/(3) w`

By applying the Pythagorean theorem:

L² + w² = 10²

Then

`\left( (4)/(3) w\right)^(2) +w^(2)=100`

Then

`(16)/(9) w^(2) +w^(2)=100`

Then

`(25)/(9) w^(2)=100`

Then

`w^2=(9*100)/(25) =(900)/(25)`

Then

w = 30/5

= 6

Then

`L = (4)/(3) *6 = (24)/(3) =8`

Perimeter = 2×(L + w)

= 2×(8 + 6)

= 2×(14)

= 28