Question

27) The area of a triangle is 150 m". The ratio of its base to its heightis 3:4. Find the length of its base.​

Answer 1

Answer :-

• Base of Triangle = 15 m
• Length (Height) of Triangle = 20 m

Given :-

• Ratio of Base and Height = 3 : 4
• Area of Triangle = 150 m²

To Find :-

• Base of Triangle = ?
• Length (Height) of Triangle = ?

Explanation :-

Let the Base and Height of the Triangle to be '3x' and '4x' Respectively.

As we Know,

$\green { \boxed { \bf \Longrightarrow \: Area \: of \: Triangle = \dfrac{1}{2} \times Base \times Height \: \Longleftarrow }}$

$\rm \hookrightarrow \dfrac{1}{2} \times B \times H = Area \: of \: Triangle$

$\rm \hookrightarrow \dfrac{1}{2} \times 3x \times 4x = 150 \: m^2$

$\rm \hookrightarrow 3x \times 4x = 150 \times 2 \: m^2$

$\rm \hookrightarrow 12x^2 = 300 \: m^2$

$\rm \hookrightarrow x^2 = \dfrac{300}{12} \: m^2$

$\rm \hookrightarrow x^2 = 25 \: m^2$

$\rm \hookrightarrow x = \sqrt{25} \: m$

$\red { \underline { \boxed { \bf \hookrightarrow x = 5 \: m }}}$

Now Substituting the value of 'x',

$\rm \bigstar \: Base = 3x = 3(5) = \red{\bold{15 \: m}}$

$\rm \bigstar \: Height = 4x = 4(5) = \red{\bold{20 \: m}}$

Hence, the Base and Height of the Triangle are 15 m and 20 m Respectively.