Question

In a parallelogram ABCD,AB=18cm,BC=12cm,AL altitude to DC and AM altitude to BC.
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If AL=64cm,find the length of AM

Answer 1

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Answer 2

Answer:  The length of AM is 96 cm.

Step-by-step explanation:  As shown in the attached figure, ABCD is a parallelogram, where AB = 18 cm and BC = 12 cm.

AL and AM are altitudes from the vertex A to the sides DC and BC respectively and AL = 64 cm.

We are to find the length of AM.

The area of a parallelogram is given by the formula

Area = base × height.

If we consider DC as the base and AL as the height, then the area of the parallelogram ABCD is given by

$Area=DC\times AL,$

and if we consider BC as the base and AM as the height, then the area of the parallelogram ABCD is given by

$Area=BC\times AM.$

Therefore, we must have

$DC\times AL=BC\times AM\\\\\Rightarrow AB\times AL=BC\times AM~~~\textup{(since the opposite sides of a parallelogram are congruent)}\\\\\Rightarrow 18\times 64=12\times AM\\\\\Rightarrow AM=\dfrac{18\times64}{12}\\\\\Rightarrow AM=96.$

Thus, the length of AM is 96 cm.