Question

15) a) A dining table is in the shape of a rectangle ABCD has sides of length (2x+12)cm and (x)cm and the length of diagonal BD is (2x+18)cm. Draw diagram and find x​

Answer 1

Answer:

AB=2x+12

AD=x

BD=2x+18

Angle A=90 degree

So by Pythagoras theorem

${bd}^{2} = {ab}^{2} + {ad}^{2}$

${(2x + 18)}^{2} = {(2x + 12)}^{2} + {x}^{2}$

${x}^{2} - 24x - 180 = 0$

${x}^{2} - 30x + 6x - 180 = 0$

$x(x - 30) + 6(x - 30) = 0$

$x = 30 \: \: and \: \: x = - 6$

But x can't be negative so x =30 cm