Question

Can you please help me

Answer 1

We have to calculate the area and perimeter of ABC.

Area:

We can calculate the area by substracting from the area of the big triangle ABD the area of the little triangle BCD. Both are right triangles.

The area of ABD is:

`A_{\text{ABD}}=(b\cdot h)/(2)=((15+5)\cdot12)/(2)=(20\cdot12)/(2)=(240)/(2)=120`

The area of BCD is:

`A_{\text{BCD}}=(b\cdot h)/(2)=(5\cdot12)/(2)=(60)/(2)=30`

Then, the area of ABC is:

`A_{\text{ABC}}=A_{\text{ABD}}-A_{\text{BCD}}=120-30=90`

The area of ABC is 90 cm^2.

Perimeter:

We calculate the perimeter by adding the length of the three sides. We know only 2 of the sides, so we have to calculate the other one (BC).

The length of BC can be calculated using Pythagorean theorem for the triangle BCD, so we can write:

`\begin{gathered} BC^2=CD^2+BD^2=5^2+12^2=25+144=169 \\ BC=\sqrt[]{169}=13 \end{gathered}`

Now, we can calculate the perimeter as:

`P_{\text{ABC}}=AB+BC+AC=25+13+15=53`

The perimeter is 53 cm.