Question

The base of a triangle field is two times its altitude. if the cost of levelling the field at ₹30 per sq m is ₹6750. find its base and height.​

Answer 1

Answer:

We know the area of a triangle =  x (base) x (altitude)

Let the altitude of the triangle = a

therefore, base length = 3a

=> area, A =  x 3a x a

=>  sq.metre

Price of levelling the field of area A = A x 30.50

Given : 30.50 A = 7350

           => A = 240.98 sq.metre

Therefore,

                 =>  a = 12.67 metre

Hence, altitude length = 12.67 metre , and base length = 38.01 metre

Step-by-step explanation:

Answer 2

Given :

• Cost of levelling = Rs.6750
• Rate of Levelling = Rs.30
• Base is two times the Altitude

To Find :

• Find the Base and Height

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SolutioN :

✴ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Area{\small_{(Triangle)}} = \dfrac{1}{2} \times Base \times Height }}}}}$

✴ Calculating the Area :

${\longmapsto{\qquad{\sf{ Area = \dfrac{Cost}{Rate} }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ Area = \dfrac{6750}{30} }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ Area = \cancel\dfrac{6750}{30} }}}} \\ \\ \\ \ {\qquad \; {\longmapsto \; {\pmb{\underline{\boxed{\red{\frak{ Area = 225 \; {m}^{2} }}}}}}}}$

✴ Let the Dimensions :

• Base = 2y
• Height = y

✴ Calculating the Value of y :

${\dashrightarrow{\qquad{\sf{ Area = \dfrac{1}{2} \times Base \times Height }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 225 = \dfrac{1}{2} \times 2y \times y }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 225 \times 2 = 1 \times 2y \times y }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 450 = 1 \times 2y \times y }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 450 = 2y \times y }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 450 = 2y^2 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \dfrac{450}{2} = y^2 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \cancel\dfrac{450}{2} = y^2 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 225 = y^2 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \sqrt{225} = y }}}} \\ \\ \\ \ {\qquad \; {\longmapsto \; {\pmb{\underline{\boxed{\purple{\frak{ y = 15 }}}}}}}}$

✴ Calculating the Dimensions :

• Base = 2y = 2(15) = 30 m
• Height = y = 15 m

✴ Therefore :

Base of the field is 30 m and its height is 15 m .

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