Answer:
Perimeter of Isosceles Triangle = 16 units
Step-by-step explanation:
Area of rectangle is given by the formula;
Area = 1/2 × base × height
From the diagram, base = 6x - 6 and height = 6x - 8
Thus,Area = 1/2 × (6x - 6) × (6x - 8)
Area = (3x - 3)(6x - 8) = 18x² - 42x + 24
Secondly, area of rectangle is given by;
Area = length x breadth
So, area of rectangle in question = (6x - 9)(3x - 2) = 18x² - 39x + 18
We are told both the area of the triangle and the rectangle are the same, so let's equate both areas;
18x² - 42x + 24 = 18x² - 39x + 18
18x² will cancel out and rearranging, we have;
24 - 18 = 42x - 39x
6 = 3x
x = 6/3
x = 2
Plugging 2 for x for the height and base of the triangle, we have;
base = 6(2) - 6 and height = 6(2) - 8
Base = 6 and height = 4
So,let's find the slant height of the isosceles triangle.
Dividing the base by 2,we have; 6/2 = 3
So,using Pythagoras theorem, let the slant height be h, so we have;
h² = 3² + 4²
h² = 9 + 16
h² = 25
h = √25
h = 5
2 slant sides of isosceles triangle are the same. So perimeter = 5 + 5 + 6 = 16 units
