Question

The perimeter of a rectangule. is 34 cm and area is 69 sqcm .. What is the length of each diagonal​

Answer 1

Given:-

• Perimeter of Rectangle = 34cm

• Area of Rectangle = 69cm²

To Find:-

• The Length of each Diagonal.

Formulae used:-

• Perimeter of Rectangle = 2 ( L + B )

• Area of Rectangle = L × B

• D² = √L ² + b²

Now,

→ Perimeter of Rectangle = 34

→ 2 ( L + B ) = 34

→ L + B = 17

→ L = 17 - B............eq.1

Therefore,

→ L × B = 69

→ 17 - B ( B ) = 69......From eq.1

→ 17B - B ² = 69

→ - ( 69 + 34B - B² ) = 0

→ B² - 17B + 60 = 0

→ B² - 12B - 5B - 60 = 0

→ B ( B - 12 ) - 5 ( B + 12 ) = 0

→ ( B - 5 ) = 0 → B = 5

→ ( B + 12 ) = 0 → B = -12

So, The Breadth of Rectangle is 5cm

Putting the value of B in eq.1

→ L = 17 - B

→ L = 12cm.

Therefore,

We also know that Diagonal of Rectangle bisect each other at right angled.

→ D² = √ L² + B²

→ D² = √ ( 12 )² + ( 5 )²

→ D² = √ 144 + 25

→ D² = √ 169

→ √D² = √169

→ D = 13cm.

Hence, The Length of Diagonal is 13cm

Answer 2

Answer:

12.28 cm

Step-by-step explanation:

P = 2(l + w) and A = lw

2(l + w) = 34 ⇔ l + w = 17 ⇒ l = 17 - w

lw = 69

(17 - w)w = 69

17w - w² = 69 ⇔ w² - 17w + 69 = 0

$w_{12}$ = [17 ± √(17² - 4×69)] / 2

$w_{12}$ = (17 ± √13) /2

$w_{1}$ ≈ (17 + 3.61) / 2 = 10.30

$w_{2}$ ≈ (17 - 3.61) / 2 = 6.695

The dimensions of the parallelogram are 10.30 cm and 6.695 cm

d = $\sqrt{10.30^2 + 6.695^2}$ = √150.913 ≈ 12.28 cm