Answer:
Length, l = 11 ft.
Width, w = 9 ft.
Step-by-step explanation:
From the given data, the area of the rectangle = 99 ft².
Area of the rectangle = Length, l X Width, w
Here, Length, l = 7 more than twice the width
⇒ Length, l = 7 + 2w
Therefore, Area, A = 99 = (7 + 2w)w
⇒ 99 = 7w + 2w²
⇒ 2w² + 7w - 99 = 0
Solve the Quadratic equation using the formula: x = 
for the quadratic equation ax² + bx + c = 0.
Therefore, w = 
Since, 
we get:
This gives two values of 'w', viz., w = 
, 
⇒ w = 
, -9.
We take the integer values.
If w = -9, then l = 2(-9) + 7
⇒ l = - 18 + 7 = - 11
Therefore, the length, l of the rectangle = - 11 ft.
and the width, w of the rectangle = - 9 ft.
Hence, the answer.
Answer:
24.8
Step-by-step explanation:
We will have to use trigonometry here to find the value of x. The first thing we can see is that we need to work out the hypotenuse. We need to chose whether to use Sin, Cos or Tan. We do that by look at the sides .
→ 'x' is the hypotenuse
→ 12 is opposite
→ The adjacent is the side that doesn't have a numerical value to we look for a formula triangle without adjacent in it
Tan = Opposite ÷ Adjacent
Sin = Opposite ÷ Hypotenuse
Cos = Adjacent ÷ Hypotenuse
We can see the Sin formula has no adjacent in it so we use that formula. However we want to work out the hypotenuse so we have to rearrange the sin formula to get hypotenuse as the subject so
Sin = Opposite ÷ Hypotenuse
Hypotenuse = Opposite ÷ Sin
→ Let's substitute in the values
Hypotenuse = 12 ÷ Sin(29)
Hypotenuse = 24.7519841
So the value of x is 24.8 to 1 decimal place
Answer:
<u>42.25π m²</u>
Step-by-step explanation:
Let's solve!
⇒ Take the radius of the lawn to be 'r'
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Then, area of the path equals :
⇒ Area of (lawn + path) - Area of lawn
⇒ π (r + 2)² - πr² = 30π
⇒ πr² - πr² + 4πr + 4π = 30π
⇒ 4πr = 26π
⇒ r = 6.5 m
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Area of the lawn :
⇒ Area = πr²
⇒ Area = π × (6.5)²
⇒ Area = <u>42.25π m²</u>
The answer is N=84 without me working it out
