Final Answer:
An isosceles triangle that has base 56 mm and perpendicular height 45 mm will have a perimeter of 162 mm.
Step-by-step explanation:
To find the perimeter of the isosceles triangle, we need to find the lengths of the two equal sides in addition to the base, which we already know is 56 mm.
Since we have the perpendicular height of the triangle, which is 45 mm, we can use the Pythagorean theorem to find the length of the equal sides.
The perpendicular height forms a right angle with the base, dividing the base into two equal parts of 56 mm / 2 = 28 mm each.
This creates two right-angled triangles within the isosceles triangle, each having a base of 28 mm (half the total base) and a height of 45 mm.
Let's call the length of one of the equal sides "L".
Using the Pythagorean theorem for one of the right triangles we have:
(base/2)^2 + height^2 = L^2
Where:
- base/2 is half the base of the full triangle (which is 28 mm)
- height is the perpendicular height of the full triangle (which is 45 mm)
Now plug in the numbers:
(28)^2 + (45)^2 = L^2
784 + 2025 = L^2
2809 = L^2
Taking the square root of both sides to find L:
L = √2809
L = 53
So, each of the equal sides of the triangle is 53 mm long.
The perimeter P of the triangle is the sum of the lengths of all three sides. Since we have two sides that are each 53 mm and one side that is 56 mm, the perimeter P is:
P = 53 + 53 + 56
P = 106 + 56
P = 162 mm
Therefore, the perimeter of the isosceles triangle is 162 mm.
Complete question:
An isosceles triangle has base 56 mm and perpendicular height 45 mm
Work out the perimeter of the large triangle.