I need to know the answer to question number 6 please and thank you
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Hello,
let's assume a=the length and b the width.
Answer:
A. 26 ft
Step-by-step explanation:
You might recognize that this triangle is a 5-12-13 triangle scaled up by a factor of 2. If so, you know immediately, that the hypotenuse is 2×13 = 26 feet in length.
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If you're not so lucky, you can write equations involving the lengths of the legs of the triangle. Let those be x and y, with x being the shorter leg. Then the Pythagorean relation tells you ...
x² + y² = (x+16)²
and the area relation tells you ...
120 = (1/2)xy
Using the second equation to write an expression for y, we have ...
y = 240/x
Substituting this into the first equation gives ...
x² + (240/x)² = (x+16)²
(240/x)² = 32x +256 . . . . subtract x²
1800 = x²(x +8) . . . . . . . . .multiply by x²/32
This is a cubic with one real root. It can be solved several ways. I like "graphing" as it is quick and easy. Trial and error also works. The factors of 1800 include 10²·18, so it is clear that x=10 is the solution.
The hypotenuse length is x+16, so is 26 feet.
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The attachment shows the graphical solution of the original two equations. This tells you the legs of the triangle are 10 and 24, so the hypotenuse will be 10+16 = 26. The 10-24-26 triangle is recognizable as a scaled version of the 5-12-13 triangle often used in math problems.
The radius of this circle is (B) 4.9 cm.
<h3>To find the radius of the circle:</h3>To solve this problem, we need to, first of all, convert the angle from radians to degrees.
data;
- length of an arc = 18cm
- angle = 7/6π rads
- π= 3.14
Length of an Arc:
The formula for the length of an arc is given:
θ/360 ×
Let's substitute the values and solve:
From the calculations above, the radius of this circle is 4.9cm.
Therefore, the radius of this circle is (B) 4.9 cm.
Know more about radius here:
#SPJ4
Complete question
A circle has a central angle measuring 7pi/6 radians that intersects an arc of length 18 cm. What is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3.14 for pi.
(A) 3.7 cm
(B) 4.9 cm
(C) 14.3 cm
(D) 15.4 cm