Question

2. Sides of two similar triangles 2 points
are in the ratio 3:5, Areas of
these triangles are in the ratio
*
25:9
3:5
9:25
5:3​

Answer 1

Given :

• Ratio of sides of the similar triangle = 3 : 5.

To find :

The ratio of area of the triangle.

Solution :

Since the two triangles are similar , we can represent the height of the triangle by a single variable.

Here let the side of the triangle be h units.

Let the Radius of first triangle be 3x and the Radius of second triangle be 5x.

So by the above information we can find the area of the triangle in terms of x and h.

Area of the first triangle :

Let's represent the area of first triangle be A.

We know the formula for area of a triangle i.e,

⠀⠀⠀⠀⠀Area = ½ × Base × Height

Now using the above formula and substituting the values in it, we get :

➠ A = ½ × b × h

➠ A = ½ × 3x × h

➠ A = 3xh/2

∴ A = 3xh/2 units².

Hence the area of the first triangle is 3xh/2.

Area of the second triangle :

Let's represent the area of first triangle be A'.

We know the formula for area of a triangle i.e,

⠀⠀⠀⠀⠀Area = ½ × Base × Height

Now using the above formula and substituting the values in it, we get :

➠ A = ½ × b × h

➠ A' = ½ × 5x × h

➠ A = 5xh/2

∴ A = 5xh/2 units².

Hence the area of the first triangle is 5xh/2.

Ratio of the two triangles :

By putting the two area together , we get :

➠ Ratio = A/A'

➠ A/A' = (3xh/2)/(5xh/2)

➠ A/A' = 3xh/2 × 2/5xh

➠ A/A' = 3xh × 1/5xh

➠ A/A' = 3 × 1/5

➠ A/A' = ⅗

➠ A : A' = 3 : 5

∴ A : A' = 3 : 5

Hence the area of the two triangles is 3 : 5.