Question

lees 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? 48 square feet 16 square feet 32 square feet 64 square feet

Explanation:

Step1: Recall the area formula for a triangle

The area formula for a triangle is \(A=\frac{1}{2}bh\). Given the original area \(A_1 = 16\) square - feet. Let the original base be \(b\) and original height be \(h\), so \(16=\frac{1}{2}bh\).

Step2: Find the area of the new triangle

The new base is \(b_2 = 2b\) and the new height is \(h_2=2h\). The area formula for the new triangle \(A_2=\frac{1}{2}(2b)(2h)\).
Simplify \(A_2\):

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Since \(16=\frac{1}{2}bh\), then \(bh = 32\). Substitute \(bh = 32\) into the formula for \(A_2\), we get \(A_2=2\times32=64\) square - feet.

Step3: Calculate the increase in area

The increase in area \(\Delta A=A_2 - A_1\).
Substitute \(A_2 = 64\) and \(A_1 = 16\) into the formula: \(\Delta A=64 - 16=48\) square - feet.

Answer:

48 square feet