the short side of an isosceles triangle is 16cm long. by increasing each side length by 24 cm doubles the perimeter.how long are the other sides of the original triangle? ..
Hi uhm,im in grade six i need help i dont understand!
To solve this problem, we can start by identifying the given information:
1. The short side of the isosceles triangle is 16 cm long.
2. By increasing each side length by 24 cm, the perimeter of the triangle doubles.
Let's denote the lengths of the other two sides of the original triangle as x. Now, we can set up an equation to represent the given information. The perimeter of a triangle is the sum of all three side lengths, so:
Perimeter of original triangle = 2 * Perimeter of increased triangle
Since the perimeter of a triangle is the sum of its side lengths, we can write:
16 + x + x = 2 * (16 + 24 + 24)
In the equation above, we substitute the known value of the short side (16 cm) and the increased side lengths (24 cm) on the right-hand side of the equation.
Now, we can simplify and solve the equation to find the length of the other sides of the original triangle.
16 + 2x = 2 * 64
16 + 2x = 128
Next, we can solve for x by isolating it on one side of the equation:
2x = 128 - 16
2x = 112
x = 112 / 2
x = 56
Therefore, the length of the other sides of the original isosceles triangle is 56 cm.
Make an equation to help you solve!
We know that:
Side1=16cm
Side2=Side3
Let's name Side1 x, and Side2 and Side3 (Because they are the same) y.
Perimeter=Side1+Side2+Side3
Perimeter=x+y+y
Perimeter=x+2y
Sub in your value for x:
P=16+2y
Now, we also know that:
2P=(Side1+24cm)+(Side2+24cm)+(Side3+24cm)
2P=x+2y+72
2P=2y+72+16
2P=2y+88
Let's isolate for P:
2P=2y+88
(2P)/2=(2y+88)/2
P=y+44
Now we can equate the two equations to find y, because P=P!
Good luck (: