Math Is Fun Forum

tina12

Member

Registered: 2007-08-03

Posts: 3

tough one im stuck on :(

Elise and David took measurements of their family's block. Their parents wanted to know the block's area in square meters. This is Elise's sketch, unfortunately she spilt some ink

They worked out the area of the block by using heron's formula:
Area of a Δ =

(a,b,c are the sides of any triangle)

Aswell as spilling ink Elise also lost their answer.
(a) Find the possible values for the diagonal

let the length of the diagonal be x

set up expressions for the area of each of the triangles using heron's formula

write down an expression for the total area of the block

B)find the largest possible area of the block.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: tough one im stuck on :(

Replace "c" with "x", or any of the letters, but stick to it one way, either "a", "b", or "c" becomes "x".
Also for largest and smallest, use 179.99999 degrees and 0.00000001 degrees for the
angles between 49 and 51 and 61 and 37 sides and you will see that for the largest side,
you have to pick 98.6 because 61 and 37 cannot reach as big as 49 and 51.
And for the smallest side for middle, you use 0 degrees and subtract the lengths of the sides.
Draw some skinny triangles to see how this works with a ruler and simple 3 and 5 inch lengths or something and measure the other side.   And make fat ones too on paper where the 3 and 5 inch lengths are almost in a straight line but not quite and measure the big other side with a ruler.
Try this out on your own.  Anyway the 61 - 37 is bigger than the 51 - 49, so you have to pick the big one, because well, you'll see it if you fiddle with a ruler on paper first with the skinniest and fattest triangles you can make.
For "a" and "b", plug in the known sides.
x is unknown, but you know the lowest and highest amounts now.

---

igloo myrtilles fourmis

tina12

Member

Registered: 2007-08-03

Posts: 3

Re: tough one im stuck on :(

hello, thanks for the reply i tried what you said but i cant quite get it done properly i'm not sure what im doing wrong i might be doing something wrong in the calculator because the answers im getting don't look right any further help would be great thanks

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: tough one im stuck on :(

One thing.
An example of 3 things in the numerator of a fraction.
3 + 5 + x
------------
     2

Is same as
3/2 + 5/2 + x/2

also same as 8/2 + x/2.

Hope that help a little.

---

igloo myrtilles fourmis

tina12

Member

Registered: 2007-08-03

Posts: 3

Re: tough one im stuck on :(

thanks for the quick reply, im still not getting it done properly, im not exactly sure what to put in the calculator because i think im doing it wrong

tina12

Member

Registered: 2007-08-03

Posts: 3

Re: tough one im stuck on :(

noone can help with the equation? it's getting really frustrating now:(