Calculate Rectangle Perimeter with Isosceles Triangle: 4 and 8 Unit Problem

Question

Look at the following rectangle:

AAABBBCCCDDDEEE84

ΔAEB is isosceles (AE=EB).

Calculate the perimeter of the rectangle ABCD.

Video Solution

Solution Steps

00:00 Find the perimeter of the rectangle
00:06 In a rectangle all angles are right angles
00:09 We'll use the Pythagorean theorem in triangle ADE
00:12 We'll substitute appropriate values and solve to find DE
00:19 We'll isolate DE
00:30 And this is the length of DE
00:42 Isosceles triangle according to given
00:48 Opposite sides are equal in a rectangle
00:52 Right angles in a rectangle
00:59 Therefore the triangles are congruent by AAS
01:05 The sides are equal because the triangles are congruent
01:16 The side equals the sum of its parts
01:27 The perimeter of the rectangle equals the sum of its sides
01:37 Let's group terms
01:47 Let's break down 48 into factors 16 and 3
01:52 Let's solve the square root of 16
01:56 And this is the solution to the problem

Answer

8+163 8+16\sqrt3