the perimeter of an isoscles triangle is 42 cm and its base is 3/2 times each of equal sides. find the length of each sides. and area
let each of the equal sides be x
then the base is (3/2)x
x+x+3x/2= 42
times 2
4x + 3x = 84
7x = 84
x = 12
sides are 12, 12, and a base of 18
we need the height for area calculation:
make a sketch showing the height, let it be h
I see:
h^2 + 9^2 = 12^2
h^2 = 108
h = √108 = 6√3
area = (1/2)(18)(6√3) = 54√3 cm^2
= appr ......
its ans is
sides are 12,12,18
and h= 71.42
my arithmetic error
144 - 81 = 63 , not 108
so height = √63 = 3√7 = 7.937
area = (1/2)(18)(3√7) = 71.435
To find the length of each side of an isosceles triangle when the perimeter and base are given, we can follow these steps:
Step 1: Let's assume that the length of each equal side of the triangle is 'x' cm.
Step 2: Since the base is 3/2 times each equal side, the length of the base will be (3/2)x cm.
Step 3: The perimeter of the triangle is the sum of all three sides. So we can write the equation:
x + x + (3/2)x = 42 cm
Simplifying the equation:
2x + (3/2)x = 42 cm
(4/2)x + (3/2)x = 42 cm
(7/2)x = 42 cm
x = (2/7) * 42 cm
x = 12 cm
Step 4: Now, we can calculate the length of the base using the formula: (3/2)x.
Base = (3/2) * 12 cm
= 18 cm
So, the length of each equal side of the isosceles triangle is 12 cm, and the length of the base is 18 cm.
To find the area of the triangle, we can use the formula:
Area = (1/2) * base * height
Since the triangle is isosceles, the height can be found using the Pythagorean theorem. Let's assume the height is 'h' cm:
h^2 = x^2 - (1/2)x^2
h^2 = (4/4)x^2 - (1/2)x^2
h^2 = (3/4)x^2
h = sqrt((3/4)x^2)
h = sqrt((3/4) * 12^2)
h = sqrt(108) cm
Now we can calculate the area using the formula:
Area = (1/2) * 18 cm * sqrt(108) cm
Area = 9 cm * sqrt(108) cm
Area ≈ 9 cm * 10.392 cm
Area ≈ 93.528 cm^2
Therefore, the length of each side of the isosceles triangle is 12 cm, and the area is approximately 93.528 cm^2.