Question

5. The base and height of a triangle are in the ratio 4: 7. If the area of the triangle is 126 m^ , find its base
and height.
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Answer 1

Given :-

• The base and height of a triangle are in the ratio 4:7
• The Area of Triangle is 126m²

To Find :-

• Measures of Base and Height

Solution :-

Let the Base be 4x

Let the Height be 7x

➞ Area of Triangle = ½ × Base × Height

➞ 126 = ½ × 4x × 7x

➞ 126 × 2 = 4x × 7x

➞ 252 = 4x × 7x

➞ 252 = 28x²

➞ 252 ÷ 28 = x²

➞ 9 = x²

➞ √9 = x

➞ 3 = x

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Verification :-

➞ Area of Triangle = ½ × Base × Height

➞ 126 = ½ × 4x × 7x

➞ 126 = ½ × 4 × 3 × 7 × 3

➞ 126 = ½ × 12 × 21

➞ 126 = ½ × 252

➞ 126 = 126

________________

Therefore :-

• Base of Triangle = 4x = 4 × 3 = 12m
• Height of Triangle = 7x = 7 × 3 = 21m

________________

★ Additional Info :

Formulas Related to Area :-

• Area of Square = Side x Side
• Area of Rectangle = Length × Breadth
• Area of Triangle = ½ × base x height
• Area of parallelogram = base x height
• Area of circle = πr²
• Area of Rhombus = ½ × product of its diagonals
• Area of Trapezium = ½ × height × sum of parallel sides
• Area of Polygon = sum of the area of all regions into which it is divided

________________

Answer 2

Answer :-

• The base and height of triangle are 12m and 21m.

Step-by-step explanation :

To Find :-

• The base and height of triangle

Solution:

Given that,

• The base and height of triangle are in the ratio of 4:7
• The area of traingle = 126m²

As we know that,

Area of triangle = 1/2 × b × h,

Where,

• b = Base
• h = Height

=> 1/2 × b × h = 126

=> 1/2 × 4x × 7x = 126

=> 1 × 4x × 7x = 126 × 2

=> 4x × 7x = 126 × 2

=> 4x × 7x = 256

=> 28x² = 256

=> x² = 256/28

=> x² = 9

=> x² = √9

=> x = 3

• The value of x is 3.

Now, The base and height of triangle is,

• Base ( b ) We assumed the base of triangle as 4x,

=> 4x

=> 4*3

=> 12m

• Height ( h ) We assumed the height of traingle as 7x,

=> 7x

=> 7*3

=> 21m

Hence,

• The base and height of triangle are 12m and 21m.