A rectangle has side (3+root2)metres and (5-root2 )metres. find the length of its diagonal
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if one side is a and other is b
then diagonal is given by √{a^2+b^2}
thrfore,, here (3+√2)^2=9+2+6√2
(5-√2)^2=25+2-10√2
add 38-4√10
diagonAl=√{38-4√10}
then diagonal is given by √{a^2+b^2}
thrfore,, here (3+√2)^2=9+2+6√2
(5-√2)^2=25+2-10√2
add 38-4√10
diagonAl=√{38-4√10}
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In a rectangle, all angles are equal to 90°
Let the name of the rectangle be ABCD.
Draw the diagonal AC
Now, triangle ABC is a right triangle, where angle B = 90° and AC is the hypotenuse.
AB² + BC² = AC²(Pythagoras theorem)
(5√2)² + (3√2)² = AC²
(25 × 2) + (9 × 2) = AC²
50 + 18 = AC²
68 = AC²
AC = √68
AC is approximately 8.25 metres.
Let the name of the rectangle be ABCD.
Draw the diagonal AC
Now, triangle ABC is a right triangle, where angle B = 90° and AC is the hypotenuse.
AB² + BC² = AC²(Pythagoras theorem)
(5√2)² + (3√2)² = AC²
(25 × 2) + (9 × 2) = AC²
50 + 18 = AC²
68 = AC²
AC = √68
AC is approximately 8.25 metres.
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