Question

1. have a rectangle with an area of 88 sq. in. and a length of 11 in., find the width. 11) if the circumference of a circle is 56.52 in, find the radius. 12) given a triangle with an area of 48 sq. in. and a height of 8 in., find its base. 13) given a triangle with a perimeter of 63 m, one side length of 18 m, and one side length of 21 m, find the third missing side length

Explanation:

1. For the rectangle problem:

• Explanation:
• Step1: Recall the area formula for a rectangle
• The area formula of a rectangle is \(A = l\times w\), where \(A\) is the area, \(l\) is the length, and \(w\) is the width. We are given \(A = 88\) square - inches and \(l = 11\) inches.
• We need to solve for \(w\). Rearranging the formula gives \(w=\frac{A}{l}\).
• Step2: Substitute the values
• Substitute \(A = 88\) and \(l = 11\) into the formula \(w=\frac{A}{l}\). So \(w=\frac{88}{11}=8\) inches.
• Answer: 8 inches

1. For the triangle area problem:

• Explanation:
• Step1: Recall the area formula for a triangle
• The area formula of a triangle is \(A=\frac{1}{2}\times b\times h\), where \(A\) is the area, \(b\) is the base, and \(h\) is the height. We are given \(A = 48\) square - inches and \(h = 8\) inches.
• We need to solve for \(b\). Rearranging the formula gives \(b=\frac{2A}{h}\).
• Step2: Substitute the values
• Substitute \(A = 48\) and \(h = 8\) into the formula \(b=\frac{2A}{h}\). So \(b=\frac{2\times48}{8}=12\) inches.
• Answer: 12 inches

1. For the circle circumference problem:

• Explanation:
• Step1: Recall the circumference formula for a circle
• The circumference formula of a circle is \(C = 2\pi r\), where \(C\) is the circumference and \(r\) is the radius. We are given \(C = 56.52\) inches.
• We need to solve for \(r\). Rearranging the formula gives \(r=\frac{C}{2\pi}\).
• Step2: Substitute the values
• Let \(\pi\approx3.14\). Substitute \(C = 56.52\) into the formula \(r=\frac{C}{2\pi}\), then \(r=\frac{56.52}{2\times3.14}=\frac{56.52}{6.28}=9\) inches.
• Answer: 9 inches

1. For the triangle perimeter problem:

• Explanation:
• Step1: Recall the perimeter formula for a triangle
• The perimeter formula of a triangle is \(P=a + b + c\), where \(P\) is the perimeter and \(a\), \(b\), \(c\) are the side - lengths. We are given \(P = 63\) meters, \(a = 18\) meters, and \(b = 21\) meters.
• We need to solve for \(c\). Rearranging the formula gives \(c=P-(a + b)\).
• Step2: Substitute the values
• Substitute \(P = 63\), \(a = 18\), and \(b = 21\) into the formula \(c=P-(a + b)\). So \(c=63-(18 + 21)=63 - 39 = 24\) meters.
• Answer: 24 meters

Answer:

1. For the rectangle problem:

• Explanation:
• Step1: Recall the area formula for a rectangle
• The area formula of a rectangle is \(A = l\times w\), where \(A\) is the area, \(l\) is the length, and \(w\) is the width. We are given \(A = 88\) square - inches and \(l = 11\) inches.
• We need to solve for \(w\). Rearranging the formula gives \(w=\frac{A}{l}\).
• Step2: Substitute the values
• Substitute \(A = 88\) and \(l = 11\) into the formula \(w=\frac{A}{l}\). So \(w=\frac{88}{11}=8\) inches.
• Answer: 8 inches

1. For the triangle area problem:

• Explanation:
• Step1: Recall the area formula for a triangle
• The area formula of a triangle is \(A=\frac{1}{2}\times b\times h\), where \(A\) is the area, \(b\) is the base, and \(h\) is the height. We are given \(A = 48\) square - inches and \(h = 8\) inches.
• We need to solve for \(b\). Rearranging the formula gives \(b=\frac{2A}{h}\).
• Step2: Substitute the values
• Substitute \(A = 48\) and \(h = 8\) into the formula \(b=\frac{2A}{h}\). So \(b=\frac{2\times48}{8}=12\) inches.
• Answer: 12 inches

1. For the circle circumference problem:

• Explanation:
• Step1: Recall the circumference formula for a circle
• The circumference formula of a circle is \(C = 2\pi r\), where \(C\) is the circumference and \(r\) is the radius. We are given \(C = 56.52\) inches.
• We need to solve for \(r\). Rearranging the formula gives \(r=\frac{C}{2\pi}\).
• Step2: Substitute the values
• Let \(\pi\approx3.14\). Substitute \(C = 56.52\) into the formula \(r=\frac{C}{2\pi}\), then \(r=\frac{56.52}{2\times3.14}=\frac{56.52}{6.28}=9\) inches.
• Answer: 9 inches

1. For the triangle perimeter problem:

• Explanation:
• Step1: Recall the perimeter formula for a triangle
• The perimeter formula of a triangle is \(P=a + b + c\), where \(P\) is the perimeter and \(a\), \(b\), \(c\) are the side - lengths. We are given \(P = 63\) meters, \(a = 18\) meters, and \(b = 21\) meters.
• We need to solve for \(c\). Rearranging the formula gives \(c=P-(a + b)\).
• Step2: Substitute the values
• Substitute \(P = 63\), \(a = 18\), and \(b = 21\) into the formula \(c=P-(a + b)\). So \(c=63-(18 + 21)=63 - 39 = 24\) meters.
• Answer: 24 meters