Question

the base and height of a triangle are in the ratio 3 : 2 and its area is 108 cm2 find its base and height math question​

Answer 1

Given :-

• ratio of base and height of the triangle is 3:2
• area of the triangle is 108 cm²

To Find :-

• base and height of the triangle ?

Solution :-

Let the base and height of the triangle is 3x and 2x

and we know that,

$\boxed{ \bold{area \: of \: \triangle = \frac{1}{2} \times b \times h }}$

$\bold{: \implies \frac{1}{ \cancel2} \times 3x \times \cancel 2x = 108 } \: \: \\ \\ \bold{: \implies 3 {x}^{2} = 108} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies {x}^{2} = \cancel \frac{108}{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies {x}^{2} = 36 }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies x = \sqrt{36} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies x = 6 }\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so, x = 6 is the common multiple of base and height

then,

• base = 3 × 6 = 18 cm
• height = 2 × 6 = 12 cm

hence, base and height of the triangle is 18 cm and 12 cm respectively

Answer 2

Answer:

Its base = 18 m

And height = 12 m

Step-by-step explanation:

Let us assume that the base and height of a triangle be 3x and 2x respectively.

Given: Area of rectangle = 108 cm²

Formula to find area of triangle:

(½ × base × height) sq. unit

According to question:

½ × 3x × 2x = 108

→ 3x² = 108

→ x² = 36

→ x² = 6²

→ x = 6

∴ Base = 3x = 3 × 6 = 18 cm

∴ Height = 2x = 2 × 6 = 12 cm