Question

Find the ratio of the areas of an isosceles triangle and the triangle when the sides are doubled

Answer 1

Answer:

4:1

Step-by-step explanation:

Let a,b,c be the sides of the triangle.

Perimeter 2s = a+b+c

Semi- perimeter, s= (a+b+c)/2

Using Hero's formula:

Area if the triangle A = root s(s-a)(s-b)(s-c)

Now, if the sides are doubled: 2a,2b,2c

Let's be the semi-perimeter.

2s' = 2a+2b+2c

s' = a+b+c

or s' = 2s

Area if the triangle, A' = root s'(s'-2a)(s'-2b)(s'-2c)

A' = root (2s)(2s-2a)( 2s- 2b)(2s-2c)

A'= root 2⁴s (s-a)( s-b)( s-c)

A' = 4 root s (s-a)(s-b)(s-c)

A'= 4A

A':A = 4:1

Ratio of area of the new triangle and old triangle is 4:1.

Answer 2

Answer:

4:1

Step-by-step explanation:

Let a,b,c be the sides of the triangle.

Perimeter 2s = a+b+c

Semi- perimeter, s= (a+b+c)/2

Using Hero's formula:

Area if the triangle A = root s(s-a)(s-b)(s-c)

Now, if the sides are doubled: 2a,2b,2c

Let's be the semi-perimeter.

2s' = 2a+2b+2c

s' = a+b+c

or s' = 2s

Area if the triangle, A' = root s'(s'-2a)(s'-2b)(s'-2c)

A' = root (2s)(2s-2a)( 2s- 2b)(2s-2c)

A'= root 2⁴s (s-a)( s-b)( s-c)

A' = 4 root s (s-a)(s-b)(s-c)

A'= 4A

A':A = 4:1

Ratio of area of the new triangle and old triangle is 4:1.