Question

If L is 30 units long and W is 10 units long, how long is the diagonal to the nearest tenth.

Answer 1

Its 31.6

Explanation:

I Checked and its True

Answer 2

Therefore the diagonal is 31.6 unit.

Explanation:

Given:

In a Rectangle

Length = L = 30 unit = Longer Leg

Width = W = 10 unit = Shorter Leg

Diagonal = d = Hypotenuse

To Find:

Relation between L ,W and d

d = ?

Solution:

In a Rectangle vertex angles are 90°

In Right Angle Triangle , By Pythagoras theorem we have

`(\textrm{Hypotenuse})^(2) = (\textrm{Longer leg})^(2)+(\textrm{Shorter leg})^(2)`

Substituting the values we get

`(d)^(2) = (L)^(2)+(W)^(2)`

i.e
`L^(2)+W^(2)=d^(2)` .........Relation between L ,W and d

Now Substituting L = 30 ,W =10 we get

`(d)^(2) = (30)^(2)+(10)^(2)\\d^(2)=1000\\Square\ Rooting\\d=\pm √(1000)\\d=31.6\ unit\ as\ d\ cannot\ be\ negative`

Therefore the diagonal is 31.6 unit.