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.

Can anyone please explain me this question​

Answer 1

Answer :-

• Base = 45m.
• Height = 15m.

Step by step explanation :-

To find :-

• Base and height.

Given that,

• The ratio of base to height of a triangular field is 3: 1.
• Cost of cultivating field at 28 per sq.m is ₹9450.

Where,

• Base = 3x
• Height = x

$\mathfrak{{ As \: we \: know \: that, }}$

$\boxed{ \sf Area = \dfrac{1}{2} \times B × H }$

Solution :-

$\implies \bf \frac{1}{2} \times 3x \times x \\ \\ \implies \bf \frac{{3x}^{2}}{2} {m}^{2}$

Area of triangle = 3x²/2 m².

Now,

$\bf Area \: of \: triangular \: field = \dfrac{9450}{28} \\ \\ \implies \bf 337.5 {m}^{2}$

According to the question,

$\implies \bf \dfrac{ {3x}^{2} }{2} = 337.5 {m}^{2} \\ \\ \bf \implies {3x}^{2} = 337.5 {m}^{2} \times 2 \\ \\ \bf \implies{3x}^{2} =675 {m }^{2} \\ \\ \bf \implies {x}^{2} = \frac{675 {m}^{2} }{3} \\ \\ \bf \implies {x}^{2} = 225 {m}^{2} \\ \\\bf \implies x = \sqrt{225} {m}^{2} \\ \\ \bf \implies x = 15 m$

Therefore,

• x = 15m
• 3x = 15 × 3 = 45m

Answer 2

Given:-

• Ratio of base to height of a triangular field is 3:1
• Cost of cultivating the field at ₹28 per sq.m is ₹9450.

To Find:-

• It's base and height

Solution:-

• Base = 3x
• Height = x

We know that,

$\large\sf\green{Area = {\frac{1}{2}×Base×Height}}$

$\sf \implies \: \frac{1}{2} \times 3x \times x \\ \\ \sf \implies \: \frac{3 {x}^{2} }{2} {m}^{2}$

Hence, Area of triangle = 3x^2/2m^2.

Now,

Area of triangular field= $\sf\frac{9450}{28}$

= 337.5m^2

According to the question,

$\sf \implies \: \frac{3 {x}^{2} }{2} = 337.5 {m}^{2} \\ \\ \sf \implies \: 3 {x}^{2} = 3375 {m}^{2} \times 2 \\ \\ \sf \implies \: {x}^{2} = 675 {m}^{2 } \\ \\ \sf \implies \: {x}^{2} = \frac{675 {m}^{2} }{3} \\ \\ \sf \implies \: {x}^{2} = 225 {m}^{2} \\ \\ \sf \implies \: x = \sqrt{225 {m}^{2} } \\ \\ \sf \implies \: x = 15m$

Therefore,

• x = 15m
• 3x = 15 ×3 = 45m