Question

A quadrilateral of perimeter 126 cm is circumscribed about a circle. Three of its sides taken in 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

We know that,

In a quadrilateral circumscribed about a circle, 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.  

Let the length of the four sides of the quadrilateral be 5x, 8x, 9x and yx.

We have

5x + 8x + 9x + yx = 126

5x + 9x = 8x + yx

=> 6x = yx => y =6

Substituting this in the first equation, we have

22x + 6x = 126

28 x =126

=> x = 4.5

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

∴ The length of the fourth side is 27 cm.

Answer 2

Hey buddy,

◆ Answer- 27 cm

◆ Solution-
Let a, b, c and d be 4 sides of quadrilateral.
From given data-
a = 5x
b = 8x
c = 9x
d = ?
s = 126 cm
Where x = common multiple

According to the Pitot Theorem,
a + c = b + d = s/2
5x + 9x = 8x + d = 126/2
14x = 63
x = 9/2

From this
8x + d = 126/2
8×9/2 + d = 63
d = 63 - 36
d = 27 cm

Thus, length of 4th side is 27 cm


Hope this helps...