Question

The lengths of two sides of the isosceles triangle are the ratio of 6:5. The perimeter of the triangle is 32cm. What is the area of the triangle?

I need this to be answered in about 10 minutes please help me understand.

Answer 1

Sorry I'm late! xx
Okay, so two of the sides in an isosceles triangle are of the same length. The lengths are either in the ratio 5:5:6 or 5:6:6
The perimeter is 32 cm

If we take the first ratio, 5:5:6, then we have 16 "parts". Let the length of each "part" be referred to as "x"
So, 16x = 32, and so x = 2

So, the ratio of the sides are 10 cm, 10 cm, 12 cm.

To find the height, "h", we need to use Pythagoras' Theorem, with 10 being the hypotenuse and 6 being the horizontal side (think of a line cutting straight down the middle of the isosceles triangle)
h^2 + 36 = 100
h = 8 cm

Area of a triangle is 0.5 x base x height. So, 0.5 x 12 x 8 = 48 cm^2

Hope I helped!! xx