Respuesta :
Let's say that the base of triangle a is 2 and the height is 3. That makes the base and height of triangle b 4 and 6. To find the area of a triangle, use the formula 1/2 multiplied by height multiplied by base. So the area of triangle a is 2 multiplied by 3 multiplied by 1/2 giving us 3. The area of triangle b is 1/2 multiplied by 4 multiplied by 6 giving us 12. Since 12 divided by 3 is 4, the area of triangle b is 4 times greater than the area of triangle a.
Answer : The area of triangle B is 4 times greater than the area of triangle A.
Step-by-step explanation :
Let the base of a triangle B be, x and the height of a triangle B be, y.
As we are given that, the base and the height of triangle A are half the base and the height of triangle B.
So, the base triangle A = [tex]\frac{x}{2}[/tex]
and, the height triangle A = [tex]\frac{y}{2}[/tex]
Now we have to determine the area of triangle A and B.
Formula used :
[tex]Area=\frac{1}{2}\times Base\times Height[/tex]
Area of triangle A = [tex]\frac{1}{2}\times \frac{x}{2}\times \frac{y}{2}[/tex]
Area of triangle A = [tex]\frac{xy}{8}[/tex]
and,
Area of triangle B = [tex]\frac{1}{2}\times x\times y[/tex]
Area of triangle B = [tex]\frac{xy}{2}[/tex]
Now we have to take ratio of triangle A and B.
[tex]\frac{\text{Area of triangle A}}{\text{Area of triangle B}}=\frac{(\frac{xy}{8})}{(\frac{xy}{2})}[/tex]
[tex]\frac{\text{Area of triangle A}}{\text{Area of triangle B}}=(\frac{xy}{8})\times (\frac{2}{xy})[/tex]
[tex]\frac{\text{Area of triangle A}}{\text{Area of triangle B}}=\frac{1}{4}[/tex]
[tex]\text{Area of triangle B}=4\times \text{Area of triangle A}[/tex]
Hence, the area of triangle B is 4 times greater than the area of triangle A.
