Question

Images explain all. ?

Answer 1

Solution 1 of 2: `color(red)("Not rounded as instructed.")`

`"area "= 1.52sqrt(66)color(white)("d")` as an exact value.

`"area "~~ 12.348color(white)("d")` to 3 decimal places

Explanation:

Have we have two legs the same length then this is what is called and Isosceles Triangle.

So this is like two Right Triangles back to back.
I assume they are called this as they have a right angle (`90^o`) in them.

The area of a triangle is `1/2" base "xx" height"`

So we need the height. We use Pythagoras to determine this:

`color(blue)("Determine the height")`

Let the height be `h`

Note that `7.6/2-> 3.8`

`h^2+(3.8)^2=5^2`

Subtract `(3.8)^2` from both sides

`h^2=5^2-(3.8)^2`

square root both sides

`h=sqrt(5^2-(3.8)^2)`

`h=sqrt(10.56)` this give a a very long decimal so switching to fractions to retain precision:

Note that `3.8 = 38/10` and that `5^2=25=2500/100`

`h=sqrt(5^2-(38/10)^2)`

`h=sqrt(2500/100-1444/100)`

`h=sqrt( 1056/100) =sqrt(1056)/sqrt(100) = sqrt(1056)/10`

If you are ever not sure about roots do a quick sketch of a prime number factor tree:

From this we have `sqrt(1056)=sqrt(2^2xx2^2xx2xx3xx11) = 4sqrt(66)`

Thus `h=(4sqrt(66))/10 = (2sqrt(66))/5`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the area")`

`"area "= 1/2xx" base"xx" height"`

`"area "= 1/cancel(2)xx7.6xx(cancel(2)sqrt(66))/5`

`"area "= 1.52sqrt(66)color(white)("d")` as an exact value.

`"area "~~ 12.348color(white)("d")` to 3 decimal places

Answer 2

Solution of 2: `color(blue)("Is rounded as instructed.")`

`"area "= 12.5" units"^2`

Explanation:

Picking up from solution 1 of 2 at the point:

`h=sqrt(5^2-(3.8)^2)`

`h~~sqrt(25 - 14.4) ~~ sqrt(10.6)` where `~~` means approximately equal

`h~~3.3`

`"area "=1/2" base"xx" height" =1/2xx7.6xx3.3 =12.5" units"^2`

All rounded as instructed.

`color(brown)("Now compare this to solution 1 of 2 and see the difference that")` `color(brown)("rounding this way makes. It is approximately "1.2%" error")`