1.

The area of a triangle is 240 cm square and one of it legs is 16 cm find the length of another leg

Answer»

Step-by-step explanation:

LET ABC be a right triangle right angles at B with AB=16 CM and BC=8 cm. Then, the LARGEST square BRSP which can be inscribed in this triangle will be as shown in figure.

Let PB=x cm. So, AP=(16−x) cm.

In △APS and △ABC,

∠A=∠A

∠APS=∠ABC (Each 90

o

)

So, △APS∼△ABC (AA similarly)

Therefore,

AB

AP

=

BC

PS

or

16

16−x

=

8

x

or 128−8x=16x

or x=

24

128

=

3

16

Thus, the side of the required square is of length

3

16 cm


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