Question

The ratio of base to height of a triangular field is 3 : 1. If the cost of cultivating the field at
28 per sq. m is 9450, find its base and height.​

Answer 1

$\sf{\huge{\underline{\purple{Given:-}}}}$

• The ratio of base to height of a triangular field is 3 : 1.

• The cost of cultivating the field at 28 per sq. m is 9450 .

$\sf{\huge{\underline{\pink{To\:Find:-}}}}$

• The base and height of triangular field.

$\sf{\huge{\underline{\blue{ Solution :-}}}}$

Let the height be x m.

Its base be 3 x m.

We, know the area of triangle = ½ × base × hieght

The area of triangular field is

➝ ½ × x × 3x

➝ $\dfrac{3x {}^{2} }{2}$ m² ___ (1)

According to the question,

The cost of cultivating the field at rupee 28 per sq. m .

& Total cost of cultivating the field = Rupee 9450 .

➝ Area of field = $\dfrac{Total\:Cost}{Cost\:Of\:Cultivation}$

➝ Area of field = $\cancel{\dfrac{9450}{28}}$

➝ 337.5m² ____(2)

Equating 1 & 2,

➝ $\dfrac{3x {}^{2} }{2}$ = 337.5

➝ 3x² = 337.5 × 2

➝ 3x² = 675

➝ x² = $\cancel{\dfrac{675}{3}}$

➝ x² = 225

➝ x = √225

➝ x = 15m

• The height = x m = 15m

• Its base = 3 x m = 3 × 15 = 75m

_______________________________________

Answer 2

Total cost is ₹9450.

Rate of cultivation is ₹28/sq.m

Area of field=9450/28 = 337.5 sq.m

Let base and height be 3x and 1x

1/2 × b × h = 337.5

1x × 3x × = 337.5×2

3x^2 = 675

x^2=675/3

x^2=225

x=√225

x=15

Base is 1×15=15

Height is 3×15=45

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