You labeled the triangle wrong sides 'a' and 'b' are supposed to be the sides that make the right angle. the other side is called the hypotenuse which is the longest side which you should have labeled 'c'
so Pythagorean theorem says
a^2+b^2=c^2
so
(2x+1)^2+(11x+5)^2=(12x+1)^2
distribute
(4x^2+4x+1)+(121x^2+110x+25)=(144x^2+24x+1)
add like terms
125x^2+114x+26=144x^2+24x+1
subtract 125x^2 from both sides
114x+26=19x^2+24x+1
subtract 114x from both sides
26=19x^2-90x+1
subtract 26 from both sides
0=19x^2-90-25
factor
(x-5)(19x+5)=0
therefor x-5=0 and/or 19x+5=0
so
x-5=0 add 5 to both sides
x=5
19x+5=0
subtract 5 from both sides
19x=-5
divide both sides by 19
x=-5/19
since side legnths can't be negative, we can cross this solution out
so x=5
subtitute
1+2x
1+2(5)
1+10=11
side a=11
11x+5
11(5)+5
55+5=60
side b=60
12x+1
12(5)+1
60+1=60
side c=61
add them all up
side a+b+c=11+60+61=132=total legnth
Answer: 3x^3 - 3x^2 - 4x - 4
Explanation:
(x - 2)(3x^2 + 3x + 2)
= x(3x^2 + 3x + 2) - 2(3x^2 + 3x + 2)
= 3x^3 + 3x^2 + 2x - 6x^2 - 6x - 4
= 3x^3 - 3x^2 - 4x - 4
Answer:
10%
Step-by-step explanation:
We know Perimeter of rectangle
= 2 (Length + Width)
If width and length are increased by 10%
New length= L + 10/100L = (1.1) L
New width = W + 10/100W = (1.1) W
Perimeter = 2 [(1.1) L + (1.1) W]
Perimeter = 2 (1.1) (L + W)
Perimeter = (2.2) (L + W)
Increase in perimeter = 2.2 (L + W) - 2 (L + W)
The increase in Perimeter = 0.2 (L + W)
Percent increase
= 0.2 (L + W)/2 (L + W) × 100
= 0.2/2 × 100
= 0.1 × 100
= 10%
I hope this helped and if it did, please mark as Brainliest.
Answer:
Step-by-step explanation:
we know that
If two triangles are similar
then
the ratio of their corresponding sides are equal and the corresponding angles are also equal
In this problem
we have
Find the value of TS
substitute
see the attached figure to better understand the problem
Answer:
58 degrees
Step-by-step explanation:
subtract 122 from 180
