Step by step
The question
Question: find the other diagonal d of a rhombus with area 45 square units and one diagonal 9.
1 Write the rule
A rhombus is half of the box around it.
The box is the two diagonals.
So A = ½ × d₁ × d₂.
Now put the numbers in: A = 45 and d₁ = 9.
Careful!
Do not forget the half.
The rhombus is only half of the box.
2 Half of the diagonal
Half of 9 is 4.5.
So 4.5 × d = 45.
3 Remove the decimals
Decimals are hard to work with.
Let's get rid of them.
We multiply every part by 10.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
Times 10 moves the point 1 place to the right.
10 × 4.5d = 45d.
10 × 45 = 450.
Write the answers.
No more decimals!
4 Remove the 45
45d means 45 times d.
We want just d.
To remove times 45, we divide by 45.
We do it on both sides, so they stay equal.
45 divided by 45 is 1.
So just d is left.
450 divided by 45 is 10.
So d = 10!
So the other diagonal is 10.
5 Check
Let's check: half of 9 times 10.
We get 45 square units, the area.
So d = 10 is right!
Let's look back.
First: write the rule.
Then: half of the diagonal.
Then: remove the decimals.
Then: remove the 45.
Last: check.