Question

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

Answer 1

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}} \\ (5)/(7.5)=(8)/(x) \\ 5x\text{ = 8 }*7.5 \\ x\text{ = }(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 =}(1)/(2)* base\text{ of big triangle}* height\text{ of big triangle} \\ A=\text{ }(1)/(2)*7.5*12 \\ A=45cm^2 \\ \end{gathered}`

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