Liz starts walking from her house at $O$ , she walks 24 m towards west to a point $A$ , then takes a sharp turn towards north and walks 7 m before stopping at the bus stop at point $B$ as shown in the diagram. Then, the distance between her house and the bus stop is(in m)

25

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Solution

The correct option is A 25
The distance between Liz's home and the bus stop is the length of the hypotenuse $O B$
$Δ O A B$ is a right triangle.
$∴$ By Pythagorean theorem
$\Rightarrow O B^{2} = A B^{2} + O A^{2}$
$\Rightarrow O B^{2} = 24^{2} + 7^{2} = 576 + 49 = 625$
$\Rightarrow O B = \sqrt{625} = 25$ m
$∴$ Distance between Liz and the bus stop is $25$ m

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Liz starts walking from her house at O, she walks 24 m towards west to a point A, then takes a sharp turn towards north and walks 7 m before stopping at the bus stop at point B as shown in the diagram. Then, the distance between her house and the bus stop is(in m) 25

The correct option is A 25The distance between Liz's home and the bus stop is the length of the hypotenuse OB ΔOAB is a right triangle. ∴ By Pythagorean theorem ⇒OB2=AB2+OA2 ⇒OB2=242+72=576+49=625 ⇒OB=√625=25 m ∴ Distance between Liz and the bus stop is 25 m

Liz starts walking from her house at $O$ , she walks 24 m towards west to a point $A$ , then takes a sharp turn towards north and walks 7 m before stopping at the bus stop at point $B$ as shown in the diagram. Then, the distance between her house and the bus stop is(in m)

25