# Thread: Diagonals of an isosceles trapezium

1. ## Diagonals of an isosceles trapezium

There is an isosceles trapezium with both the oblique sides equal to 8 cm, and the parallel sides being 4, and 9 cm respectively.

It is required to find the diagonals. Now, my answer is 10 cm. Can anyone please verify this ?

2. Hello Basal
Originally Posted by Basal
There is an isosceles trapezium with both the oblique sides equal to 8 cm, and the parallel sides being 4, and 9 cm respectively.

It is required to find the diagonals. Now, my answer is 10 cm. Can anyone please verify this ?
Not quite. If the height of the trapezium is $\displaystyle h$ cm, then
$\displaystyle h^2 = 8^2+2.5^2\;*$
and if the diagonal is of length $\displaystyle d$ cm, then
$\displaystyle d^2 = h^2 + 6.5^2$
$\displaystyle =8^2+2.5^2 + 6.5^2$
$\displaystyle \Rightarrow d = \sqrt{112.5}$
$\displaystyle =10.61$ cm (2 d.p.)

* See correction, below!

3. Originally Posted by Basal
There is an isosceles trapezium with both the oblique sides equal to 8 cm, and the parallel sides being 4, and 9 cm respectively.

It is required to find the diagonals. Now, my answer is 10 cm. Can anyone please verify this ?
This is correct.

Note to Grandad: 8cm is not the height, it is the sidelength (or maybe you're just making a mistake I don't understand)

4. Hello Laurent
Originally Posted by Laurent
This is correct.

Note to Grandad: 8cm is not the height, it is the sidelength (or maybe you're just making a mistake I don't understand)
You're right - the answer is $\displaystyle 10$ cm, although I don't understand what you mean here. I didn't say the height was $\displaystyle 8$ cm. I had a sign wrong. I should have said
$\displaystyle h^2 = 8^2 - 2.5^2$
of course!