Fill in the missing numbers to complete the linear equation that gives the rule for this table.
1 answer:
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Answer:
The length of the diagonal = 3.6 feet
Step-by-step explanation:
* Lets change the story problem to equation to solve it
- Diagonal in a rectangle is the line which joining two
opposite vertices in it
- The diagonal , the length and the width formed together right
angle triangle where the diagonal is the hypotenuse of the
triangle and the length, the width are the two legs of the
right angle
- The length of the diagonal d is √(l² + w²) ⇒ Pythagoras theorem
∴ d² = l² + w²
- The diagonal is 2 feet more than the width
∴ d = w + 2
- The length is twice the width
∴ l = w
* Lets substitute the value of d and l in the equation of Pythagoras
∴ (w + 2)² = (2w)² + w² ⇒ solve the bracket
∴ w² + 4w + 4 = 4w² + w² ⇒ collect them in one side and add like term
∴ 4w² + w² - w² - 4w - 4 = 0 ⇒ add the like term
∴ 4w² - 4w - 4 = 0 ⇒ divide all term by 4
∴ w² - w - 1 = 0 ⇒ solve the quadratic using the formula
- In ax² + bx + c = 0
∵ a = 1 , b = -1 , c = -1
∴
-The value of the width is 1.6 feet
∴ The length = 1.6 × 2 = 3.2 feet
∴ The length of the diagonal = 2 + 1.6 = 3.6 feet
Answer:
The Original length of the wire is 61.1 cm.
Step-by-step explanation:
Given:
Now it has been given that the above equation can be used to find the original length in centimeters of a wire before it was cut.
Also We need to find the original length of the wire.
From above equation we can say that;
l ⇒ Original length of the wire.
On Solving the above equation we get;
Now we will add both side by 12.5 using addition property of equality.
Hence the Original length of the wire is 61.1 cm.