Question

The area of a triangle is 30 square meters if the height is 4 m shorter than the base find the length of the base and the height of the triangle

Answer 1

Step 1:

Concept: use the formula below to find the length snd base of a triangle.

`\text{Area of a triangle = }\frac{Base\text{ }*\text{ Height}}{2}`

Step 2:

Given data

Area of a triangle = 30 square meters

Let the base = x

Height = x - 4

Step 3:

Substitute the values in the formula

`\begin{gathered} 30\text{ = }(x(x-4))/(2) \\ \text{Cross multiply} \\ x(x\text{ - 4) = 30}*2 \\ x^2\text{ - 4x = 60} \\ x^2\text{ - 4x - 60 = 0} \\ x^2\text{ -10x + 6x - 60 = 0} \\ x(x\text{ - 10)+6(x - 10) = 0} \\ (x\text{ + 6)(x - 10) = 0} \\ \text{x = -6 or 10} \\ x\text{ = 10} \end{gathered}`

Final answer

Base = 10 m

Height = 10 - 4 = 6 m