Maths Question:?

Question

Calculate the dimensions of a rectangle in which the base measures 2cm less than the height and the diagonal measures 10cms. Its an algebra question with only one letter (x).

Please no time wasters. Any time wasters will be reported to Yahoo.

I need the workings out too!!!

Answer 1

God it's so long since I did maths like this.
My first thought is to think of half of the rectangle as a right-angled triangle where the hypotenuse is 10cm
So if you use Pythagoras, you have to have the base squared plus the height squared equalling 100 (hypotenuse squared).
(Base squared) + (base + 2 squared) = 100

I can't think of the algebra to work this out, but I've just remembered that one of the standard dimensions for a right-angled triangle is 3,4,5,. Thus you can also have 6,8,10.
This would fit your sum:
The base would be 6
The height would be 8
The hypotenuse would be 10
So the rectangle would have sides measuring 6 and 8cm.

Answer 2

Firstly we need to define x
If we call the base x then the height is x + 2
We know the hypotenuse is 10 and as the shape is a rectangle then we can use Pythagarus thus

10 x 10 = 100
100 = x squared + (x+ 2) squared
Classic right angled triangle is of proportion 3 ; 4 ; 5
5 x 2 = 10 therefore
3 x 2 = 6
4 x 2 = 8
So height is 8 base is 6
Area of rectangle is 8 x 6 = 48 square centimetres.

Answer 3

as u know that rectangles are right angled at vertex ,,,so by drawing a diagonal we get two right triangles

also we know there exists a pythageors theorem in right tiangles

here we have diagonal as hypotnues = 10 cms (given)...

Let height = x

and base = x - 2

so by pythageors theorem we get

10^2 = (x-2)^2 + x^2

from here u can find the values of x and get the area of one right triangle...

after finding the area of one triangle...

area of rectangle = 2 * area of one right triangle..

hope this will help u ....

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http://www.tooldirect.co.uk/ikdeep/

Answer 4

b=h-2

b^2+h^2 == 100 (this is the Phytagoras theorem for the rectangle)

(h-2)^2+h^2 = 100
h^2 - 4h +4 +h^2 = 100
2h^2-4h+4=100
h^2-2h+2=50
h^2 - 2h-48=0

(h-8)(h+6)=0
h=8
b=6

base =6
heght =8

Answer 5

using pitagora

b=h-2

b^2+h^2 == 100

(h-2)^2+h^2 = 100
h^2 - 4h +4 +h^2 = 100
2h^2-4h+4=100
h^2-2h+2=50
h^2-2h+1=49
(h-1)^2= 49
=> h-1 = 7
=> h = 6; b = 8

Answer 6

10*10=x*x+(x+2)*(x+2)
x=6
other side = 8
10*10=6*6+8*8

Answer 7

8cm