Question

Isosceles JAM has convex angle M. JM=35,MA=4n+3, angle J=14w-1, and angle m=98 Find n. Find w. Find the perimeter of JAM

Answer 1

n = 8, w = 3 and perimeter = 122.83 units.

Explanation:

Let the angle M is the angle between the equal sides of isosceles JAM.

So, JM = MA

⇒ 35 = 4n + 3

⇒ 4n = 32

⇒ n = 8 (Answer)

Now, if ∠ J = 14w - 1 and ∠ M = 98°, then

2(14w - 1) + 98 = 180

⇒ 2(14w - 1) = 82

⇒ 14w - 1 = 41

⇒ w = 3 (Answer)

Now, draw a perpendicular bisector on JA from vertex M and it meets JA at P say.

So, Δ MPJ will be a right triangle with ∠ J = (14w - 1) = 41° {Since w = 3}

Hence,
`\cos 41 = (JP)/(JM) = (JP)/(35)`

⇒ JP = 35 cos 41 = 26.415

So, JA = 2 × JP = 52.83

So, the perimeter of Δ JAM is = 35 × 2 + 52.83 = 122.83 units (Answer)