Calculating Isosceles Triangle Side Length with Perimeter & Area

[loquetedigo]

That value has to have one side of a triangle to be isosceles knowing its perimeter and area.

Area = 40 m2
Perimeter = 30m

NOTE = You can use the online triangle calculator TrianCal to see and draw the results.
NOTE = Do not use the values ??of responses.

A) 13.33 m
B) 19.18 m or 4.54 m
C) 10.44 m or 17.72 m
D) Imposible

 

[jvicens]

Hello,

Thank you for your interesting question. Based on the given information, we can use the formula for the area of an isosceles triangle, which is (base * height) / 2. We know that the perimeter of an isosceles triangle is equal to the sum of its three sides, so we can set up the equation:

2x + y = 30 (where x is the length of the two equal sides and y is the length of the base)

We also know that the area is equal to 40 m2, so we can set up another equation:

xy = 80

Solving these two equations simultaneously, we get x = 8 m and y = 10 m. This means that the two equal sides are 8 m each and the base is 10 m.

To confirm this, we can use the online triangle calculator TrianCal and input the values for the perimeter and area. The calculator confirms that the sides of the triangle are indeed 8 m, 8 m, and 10 m, and the calculated area is 40 m2.

Therefore, the correct answer is option C) 10.44 m or 17.72 m. This means that the length of the base can be either 10.44 m or 17.72 m, while the length of the equal sides will be 8 m each. This satisfies the given conditions of having a perimeter of 30 m and an area of 40 m2.

I hope this helps clarify the solution. If you have any further questions, please feel free to ask.