Question

The quadrilateral of a perimeter 126cm is circumscribed about a circle.Three of its sides is taken in a order are in the ratio 5:8:9.What is the length of the Fourth side?​

Answer 1

Answer:

The length of the fourth side is 27 cm.

Step-by-step explanation:

Given :

Perimeter = 126 cm

Three sides are in the ratio = 5:8:9

To Find :

The length of the Fourth side.

Solution :

We know that :

In a quadrilateral, the sum of measures of any pair of opposite sides is equal to the sum of measures of the other pair of the opposite sides.  

So,

Consider the :

Length of the four sides of the quadrilateral as - 5x, 8x, 9x and yx.

Now,

$\sf\\ \\\implies 5x + 8x + 9x + yx = 126\\ \\ \implies 5x + 9x = 8x + yx\\ \\ \implies 6x = yx \\ \\ \implies y =6$

Substituting the value of y in the first equation,

$\sf\\ \\\implies 22x + 6x = 126\\ \\ \implies 28x =126\\ \\ \implies x = 4.5$

Length of fourth side = yx = 6 × 4.5 = 27

∴ The length of the fourth side is 27 cm.

$\rule{300}{1.5}$

#AnswerwithQuality.

#BAL! :)

Answer 2

Answer : 27 cm

$\rule{100}2$

step -by - step - explanation :

Given :

• Perimeter of the given quadrilateral = 126 cm
• It's three sides are in the ratio 5 : 8 : 9

To Find :

• Length of the 4th side.

SOLUTION :

We know that, In a quadrilateral,  opposite sides are equal in measures. ____ (!)

Let the common factor in their sides be " P " and the unknown side be " S "

So,

$\sf {5P}+{8P}+{9P}+{SP}=126$ (perimeter = 126) ______ (!!)

From (!),

$\sf {5P}+{9P}={8P}+{SP}$

$\sf\implies {14P}-{8P}=SP$

$\sf\implies{6P}=SP$

$\sf\therefore {S}=6$

Now, Put the value of S in the eq. ( !! )

$\sf {5P}+{8P}+{9P}+{6P}=126$

$\sf\implies {28P}={126}$

$\sf\implies P=\dfrac{126}{28}$

$\sf\therefore P={4.5}$

Finally,

To find the length of 4th side, put the value of P in "SP"

We get,

= 6 × 4.5

= 27 cm

Therefore,

The length of the fourth side of the quadrilateral is 27 cm.

$\rule{200}2$

#answerwithquality & #BAL