The expression $16 x + 11$ represents the perimeter of a quadrilateral. The lengths of the three sides are $2 x + 3, 3 x + 4$ , and $5 x - 1$ respectively. Calculate the length of the fourth side.

6 x - 5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6 x + 5

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

5 x - 6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

10 x + 6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $6 x + 5$
Perimeter of the quadrilateral $= 16 x + 11$
Total length of the three sides $= (2 x + 3) + (3 x + 4) + (5 x - 1) = 2 x + 3 x + 5 x + 3 + 4 - 1 = 10 x + 6$
Length of the fourth side = Perimeter of the quadrilateral – Sum of the lengths of the three sides
$(16 x + 11) - (10 x + 6) = 16 x - 10 x + 11 - 6 = 6 x + 5$

Suggest Corrections

Similar questions

The lengths of three consecutive sides of a quadrilateral circumscrbing a circle are 4cm, 5cm, and 7 cm respectively. Determine the length of the fourth side.

Q. The length of three concesutive sides of a quadrilateral circumscribing a circle are 4 cm, 5 cm, and 7 cm respectively. Determine the length of the fourth side.

Find the perimeter of a triangle where lengths of sides are $6 c m, 4 c m$ and $8 c m$ respectively.

The expression $15 x + 11$ represents the perimeter of the trapezoid. What is the length of the fourth side? Explain your reasoning.

The lengths of three sides of a quadrilateral are 10.6 cm, 12.7 cm, and 9.2 cm. If the perimeter of the quadrilateral is 46.9 cm, then what is the length of the fourth side?

Solution:

We know that,

Perimeter of the quadrilateral = Sum of four sides of quadrilateral

⇒ Perimeter of the quadrilateral = Sum of three sides of quadrilateral + Fourth side

⇒ 46.9 cm = (10.6 cm + 12.7 cm + 9.2 cm) + Fourth side

⇒ 46.9 cm = 32.5 cm + Fourth side

Thus, fourth side = 46.9 cm – 32.5 cm

is the answer is correct

= 14.4 cm

Join BYJU'S Learning Program

The expression 16x+11 represents the perimeter of a quadrilateral. The lengths of the three sides are 2x+3,3x+4, and 5x–1 respectively. Calculate the length of the fourth side.

The correct option is B 6x+5Perimeter of the quadrilateral =16x+11 Total length of the three sides =(2x+3)+(3x+4)+(5x–1)=2x+3x+5x+3+4–1=10x+6 Length of the fourth side = Perimeter of the quadrilateral – Sum of the lengths of the three sides (16x+11)–(10x+6)=16x–10x+11–6=6x+5

The expression $16 x + 11$ represents the perimeter of a quadrilateral. The lengths of the three sides are $2 x + 3, 3 x + 4$ , and $5 x - 1$ respectively. Calculate the length of the fourth side.