Answer
See below
Work Step by Step
(a)
The length of one leg of the right triangle is 5 cm and the hypotenuse is 13 cm. The length of the other leg will be computed by using Pythagoras theorem which states that the sum of the square of height and the square of the base will be equal to the square of the base.
Now compute the length of the other leg using Pythagoras theorem as follows:
\[\begin{align}
& \text{Heigh}{{\text{t}}^{\text{2}}}+\text{Bas}{{\text{e}}^{\text{2}}}=\text{Hypotenus}{{\text{e}}^{2}} \\
& {{\left( 5 \right)}^{2}}+{{\left( \text{Base} \right)}^{2}}={{13}^{2}} \\
& {{\left( \text{Base} \right)}^{2}}={{\left( 13 \right)}^{2}}-{{\left( 5 \right)}^{2}}
\end{align}\]
Take the square root on both sides as follows,
\[\begin{align}
& \text{Base}=\sqrt{169-25} \\
& =\sqrt{144\text{ }}\text{cm} \\
& =12\text{ cm}
\end{align}\]
Hence, the length of the other leg is \[\text{12 cm}\].
(b)
The length of one leg, the length of the other leg is 12 cm, and the hypotenuse of the right triangle is 5 cm, 12cm, and 13cm respectively. The perimeter of the triangle will be computed by adding all the sides of the right triangle.
Compute the perimeter of the right triangle using the equation as shown below:
\[\begin{align}
& \text{Perimeter of the Triangle (}P\text{)}=\text{Sum of all sides} \\
& =\left( 5+12+13 \right)\text{cm} \\
& =30\text{ cm}
\end{align}\]
Hence, the perimeter of the triangle is \[30\text{ cm}\].
(c)
The base and height of the given figure that is a triangle are 12cm and 5cm respectively. The area of the triangle will be computed by multiplying the base (b) with the height (h) and finally multiplying the resultant with the one by two to get the area of a triangle.
Compute the area of the triangle using the equation as shown below:
\[\begin{align}
& \text{Are of the Triangle (}A\text{)}=\frac{1}{2}\times b\times h \\
& =\left( \frac{1}{2}\times 12\text{ cm}\times 5\text{ cm} \right) \\
& =30\text{ c}{{\text{m}}^{\text{2}}}
\end{align}\]
Hence, the area of the triangle is \[\text{30 c}{{\text{m}}^{2}}\].
