Question

What is the length of leg y of the right triangle? (1 point)

A right triangle with hypotenuse 37 and legs 35 and y
a
2

b
8

c
12

d
35

Answer 1

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