An isosceles triangle has area of 105 ft2. if the base is 12 ft, what is the length of each leg? round your answer to the nearest tenth. a) 450.3 ft b) 14.5 ft c) 21.2 ft d) 18.5 ft

Option D) 18.5 ft

Solution:
Area of the isosceles triangle: A=105 ft^2
Base of the isosceles triangle: B=12 ft
Length of each leg of the isosceles triangle: L=?

A=BH/2
Height of the isosceles triangle (perpendicular to the base): H=?

Replacing the known values in the formula of Area:
105 ft^2=(12 ft)H/2
105 ft^2=(6 ft)H

Solving for H: Dividing both sides by 6 ft:
(105 ft^2)/(6 ft)=(6 ft)H/(6 ft)
17.5 ft=H
H=17.5 ft

Using the Pytagoras Theorem:
c^2=a^2+b^2
with:
c=L=?
a=B/2=(12 ft)/2→a=6 ft
b=H→b=17.5 ft

L^2=(6 ft)^2+(17.5)^2
L^2=36 ft^2+306.25 ft^2
L^2=342.25 ft^2
sqrt(L^2)=sqrt(342.25 ft^2)
L=18.5 ft

The length of each leg is 18.5 ft

The First answer is

VWXZ+VWXY+WYZ+VXY+VWZ+XYZ

The second possible answer is:

VWXZ+VWYZ+WYZ+VXY+VWZ+XYZ

Step-by-step explanation:

First we draw the k-maps for the function . There are two k-maps, one with V as zero while the other is V as 1. Then we combine the entries in power of 2. Remember that the function is given in maxterms form.Max-terms are those whose value is 0. So all the values other than max-values are either 1 or don't care. So we will keep these terms 0 and other as 1. The k-maps are attached in the files below. The essential prime implicants are those which are repeated in all the possible solutions.In this case Essential prime implicants are :

VWXZ+WYZ+VXY+VWZ+XYZ

http://www.32x8.com/sop5A-B-C-D-Em_4-5-7-8-10-14-15-16-17-18-21-22-23-31d_1-2-12-13option-0899788976571894282724?fbclid=IwAR2BaNgaMe0FXK1AEcwzLb1tkw5Oo-DIn-w0QNxE6ck9nYOSS1GnGtWC4SU