Question

Lee's family had a garden in the shape of a right triangle. The total area of the garden is 16 square feet. If they expand

the garden to form a triangle with twice the base
and twice the height, by how much will they increase the size of their
garden?
O 16 square feet
• 32 square feet
O
48 square feet
64 square
feet

Answer 1

48 square feet

Explanation:

Given

Before expansion

`A_1 = (1)/(2)bh` --- area of a triangle

`A_1 = 16ft^2` --- value of the area

After the base and height were expanded, the area becomes:

`A_2 = (1)/(2)BH`

Where

`B = 2b`

`H = 2h`

Substitute 2b for B and 2h for H in
`A_2 = (1)/(2)BH`

`A_2 = (1)/(2) * 2b * 2h`

`A_2 = (1)/(2) * 2*2*b*h`

`A_2 = (1)/(2) * 4*b*h`

Rewrite as:

`A_2 = 4 * (1)/(2) *b*h`

`A_2 = 4 * (1)/(2)bh`

Recall that:
`A_1 = (1)/(2)bh`

So, we have:

`A_2 = 4 * A_1`

Substitute 16 for
`A_1`

`A_2 = 4 * 16`

`A_2 = 64`

So, the area is
`64ft^2` after the dimensions were expanded

The area increased by:

`Increment = A_2 - A_1`

`Increment = 64 - 16`

`Increment = 48`

It increased by
`48ft^2`