The Length of the Given Sign = 90 inches
The Side of the Triangle can be found by Pythagorean Theorem
⇒ (Side of the Triangle)² = 40² + 30²
⇒ (Side of the Triangle)² = 1600 + 900
⇒ (Side of the Triangle)² = 2500
⇒ (Side of the Triangle) = 50
⇒ Perimeter of the Given Sign = (4 × Side of Triangle) + (2 × Length)
⇒ Perimeter of the Given Sign = (4 × 50) + (2 × 90)
⇒ Perimeter of the Given Sign = (200 + 180) = 380 in
Answer:
x = 2√30, y = 2√21
Step-by-step explanation:
You can create the following equations:
(1) from the left triangle with sides x, y and 6:
y² + 6² = x²
(2) from the right triangle with sides y, 14 and... lets call it z:
y² + 14² = z²
(3) from the big triangle:
x² + z² = 20²
(4) Combine (2) and (3) to eliminate z:
x² + y² + 14² = 20²
combine (1) and (4) to eliminate x:
y² + 6² + y² + 14² = 20²
simplify
2y² = 20² - 6² - 14² = 168
y² = 84
y = √84 = 2√21
x² = y² + 6² = 84 + 36 = 120
x = √120 = 2√30
The width is 11m and the length is 23m
Answer:
Yes, it is possible to make a topless box with a volume of 6080 cm3 out of this cardboard sheet.
The dimensions of the cardboard sheet are 54 cm x 36 cm
Step-by-step explanation:
Let
x ----> the length of the cardboard sheet
y ----> the width of the cardboard sheet
we know that
----> equation A
The volume of the topless box is
where
substitute
----> equation B
substitute equation A in equation B
Solve for y
Solve the quadratic equation by graphing
The solution is y=36 cm
see the attached figure
Find the value of x
---->
therefore
Yes, it is possible to make a topless box with a volume of 6080 cm3 out of this cardboard sheet.
The dimensions of the cardboard sheet are 54 cm x 36 cm