Step by step
The question
Question: find the other diagonal d of a rhombus with area 24 square units and one diagonal 8.
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 = 24 and d₁ = 8.
Careful!
Do not forget the half.
The rhombus is only half of the box.
2 Half of the diagonal
Half of 8 is 4.
So 4 × d = 24.
3 Remove the 4
4d means 4 times d.
We want just d.
To remove times 4, we divide by 4.
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.
4 divided by 4 is 1.
So just d is left.
24 divided by 4 is 6.
So d = 6!
So the other diagonal is 6.
4 Check
Let's check: half of 8 times 6.
We get 24 square units, the area.
So d = 6 is right!
Let's look back.
First: write the rule.
Then: half of the diagonal.
Then: remove the 4.
Last: check.