Three parallel lines - - 2 and - 3 are drawn through the vertices A- B and C of a square ABCD If the distance between - 1 and - 2 is 7 and between - 2 and - 3 is 12- then the area of the square ABCD is

The correct option is A 193 In the diagram we have that ∠ EBA and #160; ∠ FBC are complementary as are ∠ EBA and ∠ EAB .Thus ...

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Standard VII

Mathematics

Angle Bisector and It's Construction

Three paralle...

Question

Three parallel lines $ι, ι_{2} a n d ι_{3}$ are drawn through the vertices A, B and C of a square ABCD If the distance between $ι_{1} a n d ι_{2}$ is 7 and between $ι_{2} a n d ι_{3}$ is 12, then the area of the square ABCD is

193

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196

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225

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Solution

The correct option is A $193$
In the diagram we have that $∠ E B A$ and $∠ F B C$ are complementary as are $∠ E B A$ and $∠ E A B$ .
Thus $∠ E A B$ = $∠ F B C$ . We see that $△ E A B$ and $△ F B C$ are congruent by $A A A S$ . Thus
$a r e a = s^{2} = 7^{2} + 12^{2} = 193$

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Three parallel lines ι,ι2andι3 are drawn through the vertices A, B and C of a square ABCD If the distance between ι1andι2 is 7 and between ι2andι3 is 12, then the area of the square ABCD is

The correct option is A 193In the diagram we have that ∠EBA and ∠FBC are complementary as are ∠EBA and ∠EAB.Thus ∠EAB = ∠FBC. We see that △EAB and △FBC are congruent by AAAS. Thusarea=s2=72+122=193

Three parallel lines $ι, ι_{2} a n d ι_{3}$ are drawn through the vertices A, B and C of a square ABCD If the distance between $ι_{1} a n d ι_{2}$ is 7 and between $ι_{2} a n d ι_{3}$ is 12, then the area of the square ABCD is

The correct option is A $193$
In the diagram we have that $∠ E B A$ and $∠ F B C$ are complementary as are $∠ E B A$ and $∠ E A B$ .
Thus $∠ E A B$ = $∠ F B C$ . We see that $△ E A B$ and $△ F B C$ are congruent by $A A A S$ . Thus
$a r e a = s^{2} = 7^{2} + 12^{2} = 193$