Question

3. Solve the following
a. In an isosceles triangle, the base angles are equal and the vertex angle is 80°.
Find the measure of the base angle.
b. A number is 12 more than the other. Find the numbers if their sum is 48.
c. The perimeter of a rectangular swimming pool is 154 meters. Its length is 2 m
more than twice its breadth. What are the length and breadth of the pool?

Answer 1

Answer:

question2

Step-by-step explanation:

one no.x

another no. x +12

acc.to question

x+x+12=48

2x=48-12

2x=12

x=12/2

x=6

one no.6

another no.=x+12

6+12=18

Answer 2

★ Question :

In an isosceles triangle, the base angles are equal and the vertex angle is 80°. Find the measure of the base angle.

★ Answer :

To Find,

• The measure of base angles.

Solution,

Given that,

• The base angles are equal.
• The vertex angle is 80°

Let us assume the base angles of the triangle as x and x

Therefore,

x + x + 80° = 180° ..... angle sum property of triangle

⟹ x + x + 80 = 180

⟹ 2x = 180 - 80

⟹ 2x = 100

⟹ x = 100 / 2

⟹ x = 50°

Hence, the base angles are 50° and 50°.

★ Question :

A number is 12 more than the other. Find the numbers if their sum is 48.

Answer :

To Find,

• The numbers

Solution,

Given that,

• A number is 12 more than other.
• The sum of the numbers is 48

Let us assume the number as x and the other number which is 12 more than other be x + 12.

Therefore,

x + x + 12 = 48 .... [ Given ]

⟹ x + x + 12 = 48

⟹ 2x + 12 = 48

⟹ 2x = 48 - 12

⟹ 2x = 36

⟹ x = 36 / 2

⟹ x = 18

Therefore, the numbers are, by putting the values,

» The number which we assumed as x

⟹ x = 18

» The number which we assumed as x + 12

⟹ x + 12

⟹ 18 + 12

⟹ 30

Therefore, the numbers are 18 and 30.

★ Question :

The perimeter of a rectangular swimming pool is 154 meters. Its length is 2m more than twice its breadth. What are the length and breadth of the pool?

Answer :

To Find,

• The length and breadth of the pool

Solution,

Given that,

• The perimeter of the rectangular pool = 154m
• The length is 2m more than twice it's breadth

Let us assume length as 2x + 2 and the breadth as x

As, perimeter is 2 ( Length + Breadth )

⟹ 2 ( 2x + 2 + x ) = 154

⟹ 4x + 4 + 2x = 154

⟹ 6x + 4 = 154

⟹ 6x = 154 - 4

⟹ 6x = 150

⟹ x = 150 / 6

⟹ x = 25

Hence, the value of x is 25.

Therefore, the length and breadth of the rectangular pool is

» Length of the rectangular pool

⟹ 2x + 2

⟹ 2 × 25 + 2

⟹ 50 + 2

⟹ 52m

» Breadth of the rectangular pool

⟹ x = 25m

Therefore, the length and breadth of the pool are 52m and 25m