Question

the Base and height of a triangular field are in the ratio of 3 : 4 and it's area is 1014 cm square find it's base and height​

Answer 1

$\Large{\underline{\underline{\bf{Given:-}}}}$

• Base and height of triangular field are in the ratio 3:4
• Area of triangular field is 1014 cm²

$\Large{\underline{\underline{\bf{To \: Find:-}}}}$

• What is the length of base and height of triangular field ?

$\Large{\underline{\underline{\bf{Solution:-}}}}$

Let 'x' be the common in given ratios

• BASE = 3x
• HEIGHT = 4x

To find the area of triangular field, we use the formula:-

$\large{\boxed{\bf{\star \: AREA = \dfrac{1}{2} \times BASE \times HEIGHT \: \star}}}$

${\underline{\bf{According \: To \: Question:-}}}$

$\sf{\hookrightarrow 1014 = \dfrac{1}{\cancel{2}} \times 3x \times \cancel{4}x }$

$\sf{\hookrightarrow 1014 = 3x \times 2x }$

$\sf{\hookrightarrow 1014 = 6x^2}$

$\sf{\hookrightarrow \cancel\dfrac{1014}{6} = x^2}$

$\sf{\hookrightarrow 169 = x^2}$

$\sf{\hookrightarrow \sqrt{169} = x}$

$\bf{\star \: x = 13 \: \star}$

Base of the triangular field is:-

$\sf{\hookrightarrow Base = 3 \times 13}$

$\hookrightarrow$ ${\underline{\underline{\bf{ BASE = 39 \: cm }}}}$

Height of the triangular field:-

$\sf{\hookrightarrow Height = 4 \times 13}$

$\hookrightarrow$ ${\underline{\underline{\bf{ HEIGHT = 52 \: cm }}}}$

❝ Hence, the Base and Height of the triangular field are 39 cm and 52 cm respectively. ❞

______________________

Answer 2

Step-by-step explanation:

The base of triangle is 39 cm and height is 52 cm.

hope you got it.