Question

7 a square garden has an area of 400 square feet. what is the length of each side? how many feet of fencing would be needed to surround the garden?
8 a triangle has an area of 18 in². what are two possible lengths of bases and heights for the triangle?

Explanation:

Step1: Find the side length of the square garden

The area formula of a square is \(A = s^{2}\), where \(A\) is the area and \(s\) is the side - length. Given \(A = 400\) square feet. Then \(s=\sqrt{A}\).

$$s=\sqrt{400}=20$$

Step2: Calculate the perimeter of the square garden

The perimeter formula of a square is \(P = 4s\). Substitute \(s = 20\) into the formula.

$$P=4\times20 = 80$$

Step3: Use the area formula of a triangle to find base - height pairs

The area formula of a triangle is \(A=\frac{1}{2}bh\), where \(A = 18\) in². Then \(bh=2A\). So \(bh = 36\).
The factor pairs of 36 are:

• If \(b = 1\), then \(h = 36\) (since \(bh=36\))
• If \(b = 2\), then \(h = 18\)
• If \(b = 3\), then \(h = 12\)
• If \(b = 4\), then \(h = 9\)
• If \(b = 6\), then \(h = 6\)
• If \(b = 9\), then \(h = 4\)
• If \(b = 12\), then \(h = 3\)
• If \(b = 18\), then \(h = 2\)
• If \(b = 36\), then \(h = 1\)

Answer:

1. The length of each side of the square garden is \(20\) feet and \(80\) feet of fencing is needed.
2. The possible pairs of base and height for the triangle (where \(b\) is the base and \(h\) is the height) are \((1,36)\),\((2,18)\),\((3,12)\),\((4,9)\),\((6,6)\),\((9,4)\),\((12,3)\),\((18,2)\),\((36,1)\)