Find the length of each side.
Problem 1 :
Solution :
AB = x, BD = 2√2, AD = x
Using Pythagorean theorem.
AB^{2 }+ AD^{2} = BD^{2}
x^{2 }+ x^{2} = (2√2)^{2}
2x^{2} = 8
Dividing 2 on both sides.
8/2 = 2x^{2}/2
x^{2} = 4
x = 2
So, the length of each side is 2.
Problem 2 :
AB = x, BD = 40√2, AD = x
Using Pythagorean theorem
(BD)^{2} = (AB)^{2} + (AD)^{2}
(40√2)^{2} = x^{2}+ x^{2}
1600 × 2 = 2x^{2}
3200 = 2x^{2}
Dividing 2 on both sides.
3200/2 = 2x^{2}/2
x^{2} = 1600
x = 40
So, the length of each side is 40.
Problem 3 :
Solution :
AB = x, BD = 6, AD = x
Using Pythagorean theorem
(BD)^{2} = (AB)^{2} + (AD)^{2}
6^{2} = x^{2}+ x^{2}
36 = 2x^{2}
Dividing 2 on both sides.
36/2 = 2x^{2}/2
x^{2} = 18
x = √(9 × 2)
x = 3√2
So, the length of each side is 3√2.
Problem 4 :
A square has a diagonal with the length of 8√6 meters. What is the length of the sides ?
Solution :
A square has a diagonal with the length of 8√6 meters. Let s be the length of the sides of the square.
Using Pythagorean theorem.
(BD)^{2} = (AB)^{2} + (AD)^{2}
(8√6) ^{2} = s^{2} + s^{2}
64 × 6 = 2s^{2}
384 = 2s^{2}
Dividing 2 on each sides.
384/2 = 2s^{2}/2
192 = s^{2}
s = √(64 × 3)
s = 8√3
So, the length of each side is 8√3 .
Problem 5 :
A square has a diagonal 12√6. What is the measure of the sides of the square ?
Solution :
A square has a diagonal is 12√6. Let x be the sides of the square.
Using Pythagorean theorem.
(BD)^{2} = (AB)^{2} + (AD)^{2}
(12√6)^{2} = x^{2} + x^{2}
(12√6)^{2} = 2x^{2}
144 × 6 = 2x^{2}
864 = 2x^{2}
Dividing 2 on both sides.
864/2 = 2x^{2}/2
432 = x^{2}
x = √432
x = √(16 × 27)
= √(4 × 4 × 9 × 3)
= 4 × 3√3
x = 12√3
So, the measure of the sides of the square is 12√3.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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