How do I find the altitude, base and the length of a triangle?

Question

The base of an Isosceles triangle is $5\text{ cm}$ longer than the height. If the area of the triangle is $12\text{ cm}^2$. Find the height, base and the length of one of its equal sides.

Answer 1

Since, the area is given as 12, and area of a triangle is given by $$\frac{1}{2}\times \text{base}\times \text{height}=12$$

Now, you are also given that $$\text{base}=\text{height}+5$$

So, Use the second information into the formula, generate an equation and solve it!

HINT: $\text{height}=1 \text{cm}$ $\text{base}= 6 \text{cm}$

Answer 2

The equation h^2 +5h -24 = 0 is correct. Factoring by inspection: (h+8)(h-3)=0. The height is 3 cm. bh/2=12, b=8 cm. The isoceles triangle is made of a pair of 3-4-5 ratio right triangles. The equal sides are 10 cm.

Answer 3

This is a math "word problem". You express the statements mathematically and then use math facts to get a solution.

$B=H+5$

Using the formula for the area of a triangle,

$.5BH=.5(H+5)H=.5(H^2+5H)=12$

Multiplying by 2 we get a quadratic equation,

$h^2 +5h -24 = 0$

Factoring by inspection: $(h+8)(h-3)=0$. The height is 3 cm. and the base is 8 cm.

Since we are dealing with an isosceles triangle, the height can be viewed as the perpendicular bisector of the base. Using Pythagorean's Theorem, you can see that the two equal sides have a length of 5 cm.