The diagonal of a rectangle = sqrt(w^2 + l^2)
w = width
l = length
In this problem,
The diagonal = 20 in
w = x
l = 2x + 8
Let's plug our numbers into the formula above.
20in = sqrt((x)^2 + (2x + 8)^2)
Let's simplify the inside of the sqrt
20 in = sqrt(5x^2 + 32x + 64)
Now, let's square both sides.
400 = 5x^2 + 32x + 64
Subtract 400 from both sides.
0 = 5x^2 + 32x - 336
Factor
0 = (5x - 28)(x + 12)
Set both terms equal to zero and solve.
x + 12 = 0
Subtract 12 from both sides.
x = -12
5x - 28 = 0
Add 28 to both sides.
5x = 28
Divide both sides by 5
x = 28/5
The width cant be a negative number so now we know that the only real solution is 28/5
Let's plug 28/5 into our length equation.
Length = 2(28/5) + 8 = 56/5 + 8 = 96/5
In conclusion,
Length = 96/5 inches
Width = 28/5
9514 1404 393
Answer:
10) C 4/9
11) B 24
Step-by-step explanation:
10) The area ratio is the square of the ratio of side lengths. The ratio of side lengths is ...
RS/LM = 6/9 = 2/3
Then the area ratio is ...
(2/3)² = 4/9
__
11) Using the result of question 10, the area of ∆RST is ...
(4/9)(54 in²) = 24 in²
Doubling the side length multiplies the area by 4
suppose 4:4:7 be 4x, 4x, 7x
or, 15x = 180°
or, X = 180/15
or, X = 12
therefore,
4x = 4x12= 48
4x= 4x12= 48
7x= 7x12= 84
so if you plus all of them you get 180
