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Chapter 5: Q. 16 (page 200)

In鈻�SUN 鈭�S鈮�鈭�N,. Given thatSU=2x+7 ,UN=4x-1 ,andSN=3x+4 , find the numerical length of each side.

Short Answer

Expert verified

The numerical length of sidesSU ,UN andSN are 15,15 and 16 respectively.

Step by step solution

01

- Draw the possible diagram of the given problem.

The possible diagram of the given problem is:

It is being given that鈭�S鈮�鈭�N.

The sides opposite to the equal angles are also equal.

As,鈭�S鈮�鈭�N , therefore the sides opposite to these angles are also equal.

That implies,SU=UN .

02

- Find the value of x.

As,SU=UN, therefore it can be obtained that:

SU=UN2x+7=4x鈭�17+1=4x鈭�2x8=2x82=x4=x

Therefore, the value of x is 4.

03

- Find the numerical length of each sides.

Substitute 4 for x in the sides SU,UN and SN.

Therefore, it can be obtained that:

SU=2(4)+7=8+7=15

UN=4(4)鈭�1=16鈭�1=15

SN=3(4)+4=12+4=16

Therefore, the numerical length of the sidesSU ,UN and SNare 15,15 and 16 respectively.

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Most popular questions from this chapter

Quadrilateral is a parallelogram.

  1. Why is supplementary to ?
  2. Why is supplementary to ?
  3. Complete: consecutive angles of a parallelogram are ?, while opposite angles are?.

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

AD炉鈮�BC炉

What values must x and y have to make the quadrilateral a parallelogram?

What values must x and y have to make the quadrilateral a parallelogram?

Write a paragraph proof.

Given: 鈻�ABCD;鈥夆赌�鈻�BEDF

Prove: AECF is a 鈻�.

(Hint: A short proof is possible if certain auxiliary segments ate drawn.)
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