Question

Look at the rectangle and the square: Ada says that the length of diagonal SQ is two times the length of diagonal OM. Is Ada correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.

Answer 1

Answer:

No, she is wrong.

Step-by-step explanation:

A diagonal of square or rectangle is equals to hypotenuse of a triangle. So you can apply Pythagoras Theorem to solve it :

${c}^{2} = {a}^{2} + {b}^{2}$

Rectangle,

${qs}^{2} = {rs}^{2} + {qr}^{2}$

${qs}^{2} = {16}^{2} + {8}^{2} = 320$

$qs = \sqrt{320} = 17.9 \: inches$

Square,

${om}^{2} = {lo}^{2} + {lm}^{2}$

${om}^{2} = {8}^{2} + {8}^{2} = 128$

$om = \sqrt{128} = 11.3 \: inches$

Given that QS is 17.9 and OM is 11.3. So SQ is not 2 times greater than OM.

$17.9 \div 11.3 = 1.58 \: (not \: equals \: to \: 2)$