1. A rectangular field, 70m long and 50m wide, has a path of uniform width around it. If the area of the path is 896m2 , find the width of the path.
2. The base and height of a triangle are (x+3)cm and (2x-5)cm respectively. If the area of the triangle is 20cm2, find x.
3. The difference between two numbers is 3. If the square of the smaller number is equal to 4 times the larger number, find the numbers.
4. The length of a rectangle is 5cm longer than the width and its area is 66cm2. Find the perimeter of the rectangle.
5. Two positive numbers differ by 7 and the sum of their squares is 169. Find the numbers.
6. Two positive numbers differ by 5 and the square of their sum is 97. Find the numbers.
7. A piece of wire 44cm long is cut into two parts and each part is bent to form a square. If the total area of the two squares is 65cm2, find the perimeter of the two squares.
8. A particle is projected from ground level so that is height above the ground after X seconds, is given by 20x-5x (up 2) meters. After how many seconds is it 15m above the ground? Can you explain briefly why there are two possible answers?
- Answer which one you guys can! Please it’s my last choice to pass the year :(
Answers
Answer:
Draw the picture of a rectangle inside a rectangle.
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The area of the inner rectangle is 70*50 = 3500 sq. meters
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Area of the outer rectangle = (70+2x)(50+2x) = 4X^2 + 240x + 3500
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Equation:
Outer area - Inner area = 4x^2+ 240x = 1024
x^2+60x-256 = 0
(x-4)(x+64) = 0
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Positive Solution:
x = 4 meters.
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2.The base and height of a triangle are (x+3) and (2x-5)cm respectively if the area of the triangle is 20 sq.cm find x
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Area = (1/2)(base)(height)
20 cm^2 = (1/2)(x+3)(2x-5)
40 = 2x^2+x-15
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2x^2+x-55 = 0
(x-5)(2x+11) = 0
Positive solution:
x = 5
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base = x+3 = 9 cm
height = 2x-5 = 5 cm
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3.The length of a rectangle is 5cm longer than its width and its area is 66 sq.cm find the perimeter of the rectangle.
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Let width = x
The length = x+5
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Equation:
x(x+5) = 66
x^2+5x-66 = 0
(x+11)(x-6) = 0
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Positive Solution:
x = 6 cm
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Perimeter = 2(width + length)
P = 2(6 + 11)
P = 2(17)
Perimeter = 34 cm
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