Question

The height of an isosceles triangle is 2 m less than the base and the area of the triangle is

12 sqm. Find the length of its base and height.​

Answer 1

Answer:

The triangle whose two sides are equal is known as isosceles triangle.

Step-by-step explanation:

Answer 2

Answer:

Use trigonometry.

Assume a triangle with angles A,B,C and corresponding (i.e., reversely pointed by the angle) sides a, b, c.

Area of the triangle = sin(A) * b * c / 2

So this means:

12 = sin(A) * 5 * 5 / 2

sin(A) = 24/25

cos(A) = ± 7/25

then the length of the base is just

X = 5 * sin(A/2) * 2

recall that

cos(A) = 2cos(A/2)^2 - 1

let cos(A/2) = t, we have:

2t^2 - 1 = ±7/25

so,

t^2 = 16/25 or 9/25

t = ± 4/5 or ± 3/5

since A < 180 deg, A/2 < 90 deg, so t > 0, t = 4/5 or 3/5

therefore, sin(A/2) = 3/5 or 4/5

and the base X = 5 * 3/5 * 2 = 6. or, X = 5 * 4/5 * 2 = 8.

Step-by-step explanation: