Rhombus area 35, one diagonal 10, find the other

Step by step

The question

Question: find the other diagonal d of a rhombus with area 35 square units and one diagonal 10.

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 = 35 and d₁ = 10.

Careful!

Do not forget the half.

The rhombus is only half of the box.

2 Half of the diagonal

Half of 10 is 5.

So 5 × d = 35.

3 Remove the 5

5d means 5 times d.

We want just d.

To remove times 5, we divide by 5.

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.

5 divided by 5 is 1.

So just d is left.

35 divided by 5 is 7.

So d = 7!

So the other diagonal is 7.

4 Check

Let's check: half of 10 times 7.

We get 35 square units, the area.

So d = 7 is right!

Let's look back.

First: write the rule.

Then: half of the diagonal.

Then: remove the 5.

Last: check.