Question

1. the ratio of the sides of a quadrilateral are 3:4:7:10. if the perimeter of the figure is 66 feet, what are the lengths of the sides?

Explanation:

Step1: Find the sum of the ratio parts

The ratio of the sides is \(3:4:7:10\). First, we calculate the sum of the ratio terms. So, \(3 + 4+7 + 10=24\).

Step2: Determine the value of one part

The perimeter is 66 feet, which is the sum of all the sides. Since the total number of parts in the ratio is 24, we can find the value of one part by dividing the perimeter by the sum of the ratio parts. Let the value of one part be \(x\). Then, \(24x = 66\), so \(x=\frac{66}{24}=\frac{11}{4} = 2.75\) feet.

Step3: Calculate each side length

• For the first side with ratio 3: \(3\times x=3\times2.75 = 8.25\) feet.
• For the second side with ratio 4: \(4\times x = 4\times2.75=11\) feet.
• For the third side with ratio 7: \(7\times x=7\times2.75 = 19.25\) feet.
• For the fourth side with ratio 10: \(10\times x = 10\times2.75 = 27.5\) feet.

Answer:

The lengths of the sides are \(8.25\) feet, \(11\) feet, \(19.25\) feet, and \(27.5\) feet.