Questions: Use appropriate formulas to find (a) the perimeter and (b) the area of the figure. (Type an integer or a decimal.) (a) the perimeter is (b) the area is (isosceles triangle) 26 mm 48 mm 49.7 mm

Solution Steps

The given figure is a right triangle with a smaller right triangle inside it. The dimensions provided are:

• The height of the smaller triangle: 26 mm
• The base of the smaller triangle: 18 mm
• The height of the larger triangle: 49 mm

To find the perimeter of the larger triangle, we need to determine the lengths of all three sides. We already have the height (49 mm) and the base (18 mm). We need to find the hypotenuse using the Pythagorean theorem: \[ \text{Hypotenuse} = \sqrt{(\text{base})^2 + (\text{height})^2} \] \[ \text{Hypotenuse} = \sqrt{(18)^2 + (49)^2} \] \[ \text{Hypotenuse} = \sqrt{324 + 2401} \] \[ \text{Hypotenuse} = \sqrt{2725} \] \[ \text{Hypotenuse} \approx 52.2 \text{ mm} \]

Now, the perimeter of the larger triangle is: \[ \text{Perimeter} = \text{base} + \text{height} + \text{hypotenuse} \] \[ \text{Perimeter} = 18 + 49 + 52.2 \] \[ \text{Perimeter} \approx 119.2 \text{ mm} \]

The area of a triangle is given by: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] For the larger triangle: \[ \text{Area} = \frac{1}{2} \times 18 \times 49 \] \[ \text{Area} = \frac{1}{2} \times 882 \] \[ \text{Area} = 441 \text{ mm}^2 \]

Final Answer