Question

*The points (2,7), (2,2) and (14,2)form a right angled triangle, the length of its hypotenuse is …………*

1️⃣ 10
2️⃣ 12
3️⃣ 5
4️⃣ 13​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The points (2,7), (2,2) and (14,2)form a right angled triangle, the length of its hypotenuse is

1. 10

2. 12

3. 5

4. 13

EVALUATION

Let the given points are A (2,7), B(2,2) and C(14,2)

AB

$\sf{= \sqrt{ {(2 - 2)}^{2} + {(7 - 2)}^{2} } }$

$\sf{= \sqrt{ {(0)}^{2} + {(5)}^{2} } }$

= 5 unit

BC

$\sf{= \sqrt{ {(14 - 2)}^{2} + {(2 - 2)}^{2} } }$

$\sf{= \sqrt{ {(12)}^{2} + {(0)}^{2} } }$

= 12 unit

AC

$\sf{= \sqrt{ {(14 - 2)}^{2} + {(7 - 2)}^{2} } }$

$\sf{= \sqrt{ {(12)}^{2} + {(5)}^{2} } }$

$\sf{= \sqrt{144 + 25 } }$

$\sf{= \sqrt{ 169 } }$

= 13 unit

∴ AC² = AB² + BC²

∴ ABC is a right angled triangle

Length of the hypotenuse = 13 unit

FINAL ANSWER

The correct option is 4. 13

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