Question

The base and the height of Triangle A are half the base and the height of Triangle B. How many times greater is the area of Triangle B?

Answer 1

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 2

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 =
`(x)/(2)`

and, the height triangle A =
`(y)/(2)`

Now we have to determine the area of triangle A and B.

Formula used :

`Area=(1)/(2)* Base* Height`

Area of triangle A =
`(1)/(2)* (x)/(2)* (y)/(2)`

Area of triangle A =
`(xy)/(8)`

and,

Area of triangle B =
`(1)/(2)* x* y`

Area of triangle B =
`(xy)/(2)`

Now we have to take ratio of triangle A and B.

`\frac{\text{Area of triangle A}}{\text{Area of triangle B}}=(((xy)/(8)))/(((xy)/(2)))`

`\frac{\text{Area of triangle A}}{\text{Area of triangle B}}=((xy)/(8))* ((2)/(xy))`

`\frac{\text{Area of triangle A}}{\text{Area of triangle B}}=(1)/(4)`

`\text{Area of triangle B}=4* \text{Area of triangle A}`

Hence, the area of triangle B is 4 times greater than the area of triangle A.