An isosceles triangle sign is designed to have a triangular printed area of 600

Question

An isosceles triangle sign is designed to have a triangular printed area of 600 in.^2 (shaded area with a base length of a and height of h in the figure). As shown in the figure, there is a 2-in. gap between the sides of the triangles. Write a MATLAB program that determine the dimensions a and h such that the overall area of the sign will be as small as possible. In the program define a vector a with values ranging from 10 to 120 with increments of 0.1. Use this vector for calculating the corresponding values of h and the overall area of the sign. Then use MATLAB's built-in function min to find the dimensions of the smallest sign.

Explanation / Answer

clear all
clc

% a Base of triangle, h height of triangle
a=10:0.1:120;
% S, Area of shaded region
S=600;
h=(2*S)./a;
plot(a,h)
ylabel('Height [h]');
xlabel('Base [a]');
figure
% A, Area of over all triangle
a=a+4;
h=h+4;
A=(1/2).*a.*h;
plot(a,A)

ylabel('Total Area[A]');
xlabel('Base [a]');
% Minimum Total Area, Am
Am=min(A)

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