Question

The length of the diagonal of a rectangle is 10cm. If the length is 2cm longer than its width, find the length and the width of the rectangle.​

Answer 1

Explanation:

BD is the diagonal =10cm

Breadth=x

length =x+2

In triangle ABD

BD2=AB2+AD2

100=x2+(x+2)2

=x2+x2+4+4x

=2x2+4+4x

96=2x2+4x

x2+2x-48=0

x2+8x-6x-48=0

x(x+8)-6(x+6)=0

(x+8)(x-6)=0

x=-8,x=6

width=6cm

length=6+2=8 cm

Answer 2

Explanation:

if you divide the rectangle into half, you'll see a right angled triangle and immediately recognise the use of Pythagoras theorem.

Substitute them into the formula

`{a}^(2) + {b}^(2) = {c}^(2)`

x as a, x+2 as b and 10 as c