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Standard XII

Mathematics

Condition for Two Lines to Be Perpendicular

The figure ab...

Question

The figure above shows three squares with sides of length $5, 7$ and $x$ , respectively. If $A, B$ , and $C$ lie on the line $l$ , what is the value of x ?

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Solution

The figure shows squares then by the property of a square all the sides must be equal.
Slope of the line $l$ =Slope of the line $A B =$ Slope of the line $B C$ since the points $A, B, C$ lie on the same line
$\Rightarrow \frac{2}{5} = \frac{y}{7}$
$\Rightarrow y = \frac{7 \times 2}{5} = \frac{14}{5}$
We have $x = 7 + \frac{14}{5} = \frac{35 + 14}{5} = \frac{49}{5}$

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The figure above shows three squares with sides of length 5,7 and x, respectively. If A,B, and C lie on the line l, what is the value of x ?

The figure shows squares then by the property of a square all the sides must be equal.Slope of the line l=Slope of the line AB= Slope of the line BC since the points A,B,C lie on the same line⇒25=y7⇒y=7×25=145We have x=7+145=35+145=495

The figure above shows three squares with sides of length $5, 7$ and $x$ , respectively. If $A, B$ , and $C$ lie on the line $l$ , what is the value of x ?