The base of an isosceles triangle is 15mm long and the altitude is 8mm. What is the length of the legs of the triangle? Round your answer to the nearest tenth.

10.97 mm

Step-by-step explanation:

Apply the formula for finding Pythagoras theorem;

Hypotenuse^2 = Base^2 + Height^2

Hyp^2 = 7.5^2 + 8^2

Hyp^2 = 120.25

Hyp =√120.25

Hyp = 10.97 mm

do you have the measurements?

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240