I need help with geometry

Mathematics

1 answer:

GREYUIT [131]2 years ago

6 0

9514 1404 393

Answer:

Step-by-step explanation:

Attached is a copy of the figure with some of the clutter removed. The congruent angles marked with a single arc, and the parallel lines are given.

The angles marked with a double arc are congruent because they are alternate interior angles where transversal XZ crosses parallel lines XW and YZ. Of course, side XZ is congruent to itself.

Hence we have two angles and a side not between them that are congruent. We can declare ∆XWZ ≅ ∆ZYX by the AAS postulate. (choice A)

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The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm2/m

Mnenie [13.5K]

Answer:

The base is reducing at a rate of 3.4cm per min.

Step-by-step explanation:

Let The Height of the Triangle, h

Area of the triangle = A

Area of a Triangle, $A= \frac{1}{2}bh$

When $A=190 cm^2, h=10cm$

$190= \frac{1}{2}*b*10\\b=38cm$

$\frac{dA}{dt}=\frac{1}{2}h\frac{db}{dt}+ \frac{1}{2}b\frac{dh}{dt}\\\frac{dh}{dt}=1 cm/min, \frac{dA}{dt}=2cm^2/min,$

$2=\frac{1}{2}*10*\frac{db}{dt}+ \frac{1}{2}*38*1\\2=5\frac{db}{dt}+19\\2-19=5\frac{db}{dt}\\-17=5\frac{db}{dt}\\\frac{db}{dt}=-\frac{17}{5} =-3.4 cm/min$