Question

 The base and the height of a triangle are in the ratio 3 : 2. If its area is 75 cm², find its base and height.​

Answer 1

Answer:

The base and the height of the triangle are 15 cm and 10 cm respectively.

Step-by-step explanation:

Given:

The ratio of the base (b) and height (h) = 3 : 2

Area of the triangle = 75 cm²

To find out:

The value of the base and height.

Solution:

Let 'x' be the ratio

Then the ratio of the base = 3x

The ratio of the height = 2x

The formula to find the area (A) of the triangle is given as,

   $A = \dfrac{1}{2} bh$

Now substitute the values to find 'x'. Therefore,

 ⇒   $75 = \dfrac{1}{2} ( 3x\times 2x)$

       $2\times 75 = 6x^{2} \\\\150 = 6x^{2}\\\\x^{2} =\dfrac{150}{6}$

          = 25

        x = √25

        x = 5

Hence, base = 3 × 5 = 15 cm and height = 2 × 5 = 10 cm.