Question

The base & height of a triangle are in a ratio of 2:3. If the area of triangle is 108 cm sq find its base & height

Answer 1

Answer:

Given :-

• The base & height of a triangle are in the ratio of 2 : 3.
• The area of a triangle is 108 cm².

To Find :-

• What is the base & height.

Formula Used :-

$\clubsuit$ Area Of Triangle Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Area_{(Triangle)} =\: \dfrac{1}{2} \times Base \times Height}}}\: \: \: \bigstar$

Solution :-

Let,

$\mapsto \bf Base_{(Triangle)} =\: 2x\: cm$

$\mapsto \bf Height_{(Triangle)} =\: 3x\: cm$

Given :

• Area of a triangle = 108 cm²

According to the question by using the formula we get,

$\implies \bf Area_{(Triangle)} =\: \dfrac{1}{2} \times Base \times Height$

$\implies \sf 108 =\: \dfrac{1}{2} \times 2x \times 3x$

$\implies \sf 108 =\: \dfrac{1}{2} \times 6x^2$

$\implies \sf 108 \times \dfrac{2}{1} =\: 6x^2$

$\implies \sf \dfrac{108 \times 2}{1} =\: 6x^2$

$\implies \sf \dfrac{216}{1} =\: 6x^2$

$\implies \sf 216 =\: 6x^2$

$\implies \sf \dfrac{\cancel{216}}{\cancel{6}} =\: x^2$

$\implies \sf 36 =\: x^2$

$\implies \sf \sqrt{36} =\: x$

$\implies \sf 6 =\: x$

Hence, the required base and height of a triangle are :

❒ Base Of Triangle :

$\dashrightarrow \sf Base_{(Triangle)} =\: 2x\: cm$

$\dashrightarrow \sf Base_{(Triangle)} =\: (2 \times 6)\: cm$

$\dashrightarrow \sf\bold{\red{Base_{(Triangle)} =\: 12\: cm}}$

❒ Height Of Triangle :

$\dashrightarrow \sf Height_{(Triangle)} =\: 3x\: cm$

$\dashrightarrow \sf Height_{(Triangle)} =\: (3 \times 6)\: cm$

$\dashrightarrow \sf\bold{\red{Height_{(Triangle)} =\: 18\: cm}}$

$\therefore$ The base and height of a triangle is 12 cm and 18 cm .

Answer 2

Answer:

Base = 12cm

Height = 18cm

Step-by-step explanation:

Please see photo