Question

?

8. The base and height of a triangle are in the ratio 2 : 3 and its area is 48 cm2

. Find its

base and height ​

Answer 1

Answer:-

Let's take a common factor between the ratios

Let the common factor be $x$

So,

Base : $2x$

Height : $3x$

We know

Area of a triangle = $\frac{1}{2}$ × base × height

$48 = \frac{1}{2} \times 2x \times 3x$

$= > 48 = \frac{ {6x}^{2} }{2}$

$= > 48 \times 2 = {6x}^{2}$

$= > \frac{48 \times 2}{6} = {x}^{2}$

$= > 16 = {x}^{2}$

$= > {x}^{2} = 16$

$= > x = \sqrt{16}$

$= > x = \sqrt{4 \times 4}$

$= > x = 4$

So now let's put the values according to the ratios

Base : $2x$ = 2 × 4 = 8

Height : $3x$ = 3 × 4 = 12

Answer: The base and height is 8 and 12 respectively.

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Answer 2

Given :

• The Base and Height of the triangle are in the ratio of 2:3. And, area of the triangle is 180 cm².

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To Find :

• The Base and Height of triangle.

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Solution :

Let the Base and Height of the triangle be 2x and 3x respectively.

As we know that,

★ Area of triangle = 1/2 × (Base) × (Height)

→ 108 = 1/2 × (2x) × (3x)

→ 108 = 3x²

→ x² = 108/3

→ x² = 36

→ x = √36

→ x = 6

Hence,

➠ Base of triangle, 2x = 2 × (6) = 12 cm

➠ Height of triangle, 3x = 3 × (6) = 18 cm