Explanation

Make b the same in both ratios:  

a : b = 4 : 5 = 12 : 15

b : c = 3 : 2 = 15 : 10

So a : b : c = 12 : 15 : 10

Therefore a : c = 12 : 10 = 6 : 5

Last verified on 07-05-2026

Explanation

a : b = 2 : 3

b : c = 3 : 4

Since the value for b is 3 in both, just chain them:  

a : b : c = 2 : 3 : 4

Last verified on 06-05-2026

Explanation

For 2x² - 3x + 1 = 0:  

Sum = 3/2, Product = 1/2  

Let roots be α, β. Then new roots are 1/α, 1/β  

New sum = 1/α + 1/β = (α + β)/αβ = (3/2) / (1/2) = 3  

New product = 1/αβ = 1/(1/2) = 2  

New equation: x² - (sum)x + product = x² - 3x + 2 = 0  

So a:b:c = 1:-3:2

Last verified on 06-05-2026

Explanation

Make b the same in both ratios  

a:b = 3:4  

b:c = 2:5 → multiply by 2 → b:c = 4:10  

Now a:b:c = 3:4:10  

So a:c = 3:10

Last verified on 04-05-2026

Explanation

For similar triangles: area ratio = (side ratio)²  

(side ratio)² = 9/16  

side ratio = √9/16

side ratio = 3/4

Last verified on 04-05-2026