So leangh of ladder=2x+1
bottom edgre=x-1
wall edge=2x
so therefor, since this is a right triangle, use pythagorean theorem
a^2+b^2=c^2
c=hypotonues=longest side
b and a=sides touching the right angle
so x-1 and 2x are a and b
2x+1=c
subsitute
(x-1)^2+(2x)^2=(2x+1)^2
x^2-2x+1+4x^2=4x^2+4x+1
add like terms
5x^2-2x+1=4x^2+4x+1
subtract 1 from both sdies
5x^2-2x=4x^2+4x
subtract 4x from both sdies
5x^2-6x=4x^2
subtract 4x^2 from both sides
x^2-6x =0
factor out the x using distributive property which is
ab+ac=a(b+c)
x^2-6x=x(x-6)
(x)(x-6)=0
if xy=0 then assume x and/or y=0
x=0
we remember that one of the side legnths is 2x and if x=0 then the side legnth=0 which is not possible, so we discard
x-6=0
add 6 to both sides
x=6
subsitute and solve
legnth of ladder=2x+1
x=6 subsitute
2(6)+1=12+1=13
legnth of ladder =13 feet
height=2x
2(6)=12
height=12 feet
base=x-1
6-1=5
legnth of ladder=13 feet
height=12 feet
base=5 feet
A. 50 divided by .6 is 30 so .6
B. x=9 y=30
20/100=x/321
20 x 321=100x
20 x 321=6420
6420/100=64.2
See the attached picture.
<span>you are given that ABCE is an isosceles trapezoid. </span>
<span>you are given that AB is parallel to EC. </span>
<span>this means that AE is congruent to BC. </span>
<span>you are given that AE and AD are congruent. </span>
<span>triangle EAD is an isosceles triangle because AE and AD are congruent. </span>
<span>this means that angle 1 is equal to angle 3. </span>
<span>since angle 1 is equal to angle 2 and angle 3 is equal to angle 1, then angle 3 is also equal to angle 2. </span>
<span>this means that AD and BC are parellel because their corresponding angles (angles 3 and 2) are equal. </span>
<span>since AB is parallel to EC and DC is part of the same line, than AB is parallel to DC. </span>
<span>you have AB parallel to DC and AD parallel to BC. </span>
<span>if opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram. </span>
<span>that might be able to do it,depending on whether all these statements are acceptable without proof. </span>
<span>they are either postulates or theorems that have been previously proven. </span>
<span>if not, then you need to go a little deeper and prove some of the statements that you used.. </span>
here's my diagram.
<span>this is not a formal proof, but should give you some ideas about how to proceed. </span>
<span>you can also prove that angle 4 is equal to angle 2 because they are alternate interior angles of parallel lines. </span>
<span>you can also prove that angle 6 is equal to angle 5 because they are alternate interior angles of parallel lines. </span>
Hi there!
The formula for the lateral area of a cylinder is LA = 2 x pi x r x h. Using this formula, we can plug in the given values and solve for the lateral area.
WORK:
LA = 2pi x r x h
LA = 2pi x 4.5 x 17
LA = 153pi mm^2
The correct answer is the first option - 153pi mm^2
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
