Question

the base of an isosceles triangle whose area is 12 cm square and the equal side is 5 cm each is

Answer 1

This is a great problem and I am sure that it would give many of my students immense self satisfaction to solve it by themselves.

This is how I would do it.

So that (b + 4)(b – 4)(b + 3)(b – 3) = 0

Neglecting the negative values, b could be 3 giving h = 4

or b could be 4 giving h = 3

This means the whole base could be 6 and the height is 4

OR the whole base could be 8 and the height is 3

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Sairishita Manne

There are actually two solutions to this problem!

We know that A=12bh=12, and that a vertical line from the apex of the triangle to the base will divide it into two congruent right triangles, each with base 12b, height h, and hypotenuse 5.

However, to make the math a little simpler, I’m going to define a new variable, c=12b, so A=ch=12, and each right triangle has a height of c.

From there, the Pythagorean theorem tells us:

c2+h2=52

By this point, you might have already figured out what two numbers multiply to make 12, and make a Pythagorean triple with 5, but let’s continue!

Solving the area equation for h, we get h=12c. Substituting that expression into the Pythagorean equation, we get:

c2+(12c)2=25