Question

The triangles at the top are similar. What is the area of the large triangle

Answer 1

Solution

Step 1

find the value of x on the bigger triangle using the ratio of similar sides since both triangles are similar.

$\begin{gathered} \frac{base\text{ of small triangle}}{base\text{ of big triangle }}=\frac{height\text{ of small}}{height\text{ of big triangle}} \\ \frac{5}{7.5}=\frac{8}{x} \\ 5x\text{ = 8 }\times7.5 \\ x\text{ = }\frac{60}{5} \\ x\text{ =12cm} \end{gathered}$

Step 2

Use the expression for the area of a triangle to find the area of the big triangle

$\begin{gathered} \text{The area of a triangle =}\frac{1}{2}\times base\text{ of big triangle}\times height\text{ of big triangle} \\ A=\text{ }\frac{1}{2}\times7.5\times12 \\ A=45cm^2 \\ \end{gathered}$

Hence the area of the big triangle is 45 cm squaredT. Option D is right