Question

The total value of an isosceles triangular plot at the rate of Rs 125 per square meter is Rs 50000. If the length of its base is 40 meters, then what is the length of each of the arms equal to the plot?

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Answer 1

AnswEr :

⋆ Reference of the Image is in Attachment :

• Value of Isosceles triangular plot is Rs.50,000 at the Rate of Rs. 125 per m².
• Length of its Base is 40 metre.
• Find the Equal length of Triangle.

First of all Draw a Perpendicular AD on the Base BC of Isosceles Triangle. It will Bisect BC into two Equal Parts i.e. BD = DC = 20 m

Let's take AD be y m, and Equal Sides AB and AC be x m.

• In Right Angle Triangle ADC ;

→ AC² = AD² + DC²⠀[ By Heron's Formula ]

→ ( x )² = ( y )² + ( 20 )²

→ x² = y² + 400⠀⠀⠀⠀⠀—eq.( I )

• According to the Question Now :

⇒ Area of ∆ABC × Rate = Total Value

⇒ (1 /2 × Base × Height) × 125 = 50,000

⇒ 1 /2 × BC × AD = 50,000 /125

⇒ 1 /2 × 40 × y = 400

⇒ 20 × y = 400

• Dividing Both term by 20

⇒ y = 20 m = AD ( Height )

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• Putting the Value of y in eq.( I ) :

⇒ x² = y² + 400

⇒ x² = ( 20 )² + 400

⇒ x² = 400 + 400

⇒ x² = 800

⇒ x = √800

⇒ x = 20√2 m ( Equal Sides )

∴ Equal Sides of Triangular plot is 20√2 m

Answer 2

Answer:

Referring to the attachment.

■ Given:-

•Total value of an isosceles triangle is 50000 at the rate of Rs.125 m^2.

•Length of its base is 40 m.

■ To find out:-

•Length of the equal parts of the triangle.

■ Solution:-

Draw a perpendicular AD above BC which will make BC into two parts BD and CD.Where, BD =CD =20 m.

Let's take AD =x and the equal parts AB and AC =y

According to Heron's right angle triangle formula,

AC^2 =AD^2 + BC^2

or, y^2 = x^2+ 40^2

So, y^2=x^2+400...........(i)

According to the question,

Area of ∆ABC × Rate = Total Value.

or, (1/2 × base × height)× 125 =50000

or, (1/2 × 40 × X)×125 =50000

or, 20X ×125 =50000

or, 2500X =50000

or, X =50000/2500

So,X =20 m.

Putting the value of X in the (i) equation,

y^2 =20^2+400

or, y=400+400

or, y^2=800

or, y =√800

or, y =√400×2

or, y =√20^2 ×2

or, y =20√2 m.

Therefore, the length of the arms equal to the plot is 20√2 m.

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Hope it helps you!!!