Question

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.

Answer 2

Given:-

• Area of a triangle is 150 m².
• Ratio of its base to its heightis is 3:4.

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To find:-

• Length of its base.

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Solution:-

Let,

• the base and height of a triangle be 3x and 4x.

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★Formula used:-

Area of triangle = 1/2 × b × h

⠀

→ 150 = 1/2 × b × h

→ 150 = 1/2 × 3x × 4x

→ 100 = 4x²

→ x = √25

→ x = 5 cm

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Now,

• Putting the value of x.

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→ 3x = 3 × 5 = 15 cm

→ 4x = 4 × 5 = 20 cm

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Hence,

• the Base and Height of the Triangle are 15 m and 20 m.

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⛦More Formulas:-

→ Area of rectangle = length × breadth sq.units

→ Perimeter of square = 4 × side units

→ Area of square = side × side sq.units

→ Perimeter of circle = 2πr units

→ Area of circle = πr² sq.units

→ Perimeter of parallelogram = 2 × (a + b) units

→ Area of parallelogram = base × height sq.units

→ Perimeter of rhombus = 4 × side units

→ Area of rhombus = 1/2 × diagonal (1) × diagonal (2) sq.units

→ Perimeter of equilateral triangle = 3 × side units

→ Area of equilateral triangle = √3/4 × a² = 1/2 × side × height sq.units

→ Perimeter of trapezoid = (Sum of all sides) units

→ Area of trapezoid = 1/2 × height × (sum of parallel sides) sq.units