Question

The base and height of a triangle are in the ratio 2:3 and its area is 48cm² find it base and height​

Answer 1

Answer:

this is the ans........

Answer 2

Answer :

The base is 12cm and the height is 8cm

Given :

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

To Find :

• The base and height of the triangle

Formula to be used :

If the base and height of a triangle are given then the expression for its area is given by :

$\sf \bullet \: \: Area \: of \: the \: triangle = \dfrac{1}{2}\times base \times height$

Solution :

Let us consider the base be x and height be y

According to question :

$\sf \implies x : y = 2:3 \\\\ \sf \implies \dfrac{x}{y}= \dfrac{2}{3} \\\\ \sf \implies x = \dfrac{2}{3}y ........(1)$

Now we are given area of the triangle is 48cm²

$\sf \implies \dfrac{1}{2}\times x \times y = 48\\\\ \sf Putting \: the \: value \: of \: x \: from \: (1) \\ \sf \implies \dfrac{1}{2}\times \{ \dfrac{2}{3}y \} \times y = 48 \\\\ \sf \implies y^{2} = 3\times 48 \\\\ \sf \implies y^{2} = 144 \\\\ \sf \implies y = 12cm$

Using the value of y in (1) we have :

$\sf \implies x = \dfrac{2}{3}\times 12 \\\\ \sf \implies x = 2 \times 4 \\\\ \sf \implies x = 8cm$

Thus the base is 8cm and the height is 12cm