# Math

posted by .

Suppose an isosceles triangle has perimeter 10 cm. Find an expression for its area A as a function of the
length of its base b (assume that the other two sides are the sides of equal length). What is the domain
of A?

• Math -

let each of the equal sides be x
so 2x + b = 10
x = (10-b)/2

let the height be h
h^2 + (b/2)^2 = [(10-b)/2]^2
h^2 + b^2/4 = (100 - 20b + b^2)/4
h^2 = (100-20b+b^2-b^2)/4
h^2= (100-20b)/4
h = √(100-20b)/2

area = (1/2)bh
= (1/2)b(√(100-20b)/2
= (1/4) b√(100-20b)

check my arithmetic

## Similar Questions

1. ### calculus

Find the lenght of the sides of an isosceles triangle with a given perimeter if its area is to be as great as possible. let k be the the length of the two iso sides, so the other side is P-2k. Call that the base. Using Heron's formula: …
2. ### Math--Area

Find the area of each regular polygon to the nearest tenth. Octagon with side length of 10 kilometers. Heres what I tried; but I don't know if im on the right track. Area=1/2 * Perimeter* Apothem Perimeter=base of octagon* number of …
3. ### geometry

The perimeter of an isosceles triangle is 37 in. The lengths of the two equal legs are 6 in. less than 3 times the length of the base. Find the lengths of the three sides. 37=2L+2W W=3W-6 do i have this equation wrote right when i …
4. ### geometry

The perimeter of an isosceles triangle is 42 cm . its base is 2/3 times the sum of the equal sides . find the length of each side and the area of the triangle.
5. ### math

how do i get the answer to this question. the base of an isosceles triangle is half as the two equal sides. write the area of the triangle as a function of the length of the base
6. ### algebra

This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 can be used to find the side lengths. If one of …
7. ### algebra

an isosceles triangle is one in which two sides are the same length. The perimeter of an isosceles triangle is 36cm if the length of the congruent sides is 4 times the length of the third side, find the dimentions of the triangle
8. ### Algebra 2

The base of an isosceles triangle is 1/4 as long as the two equal sides. Write the area of the triangle as a function of the length of the base.
9. ### algebra,

This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 can be used to find the side lengths. If one of …
10. ### Math

Length of equal sides of an isosceles triangle is 4cm less than twice the length of third side.find length of equal sides if perimeter of the triangle is 57 cm

More Similar Questions