Question

the right triangle below is dilated by a scale factor of 5. find the perimeter and area of the right triangle below, as well as the perimeter and area of the dilated right triangle. express your answers as whole numbers, decimals, or fractions in simplest terms (no mixed numbers). figures are not necessarily drawn to scale.

perimeter of given right triangle
units
perimeter of dilated right triangle
units
area of given right triangle
units²
area of dilated right triangle
units²

Explanation:

Step1: Perimeter of given triangle

Sum the sides: \(8 + 15 + 17\)
\(8 + 15 + 17 = 40\)

Step2: Area of given triangle

Use area formula for right triangle: \(\frac{1}{2} \times \text{base} \times \text{height}\)
\(\frac{1}{2} \times 8 \times 15 = 60\)

Step3: Perimeter of dilated triangle

Scale factor is 5, so perimeter scales by 5: \(40 \times 5\)
\(40 \times 5 = 200\)

Step4: Area of dilated triangle

Area scales by square of scale factor (\(5^2 = 25\)): \(60 \times 25\)
\(60 \times 25 = 1500\)

Answer:

Perimeter of given right triangle: \(40\) units
Area of given right triangle: \(60\) units²
Perimeter of dilated right triangle: \(200\) units
Area of dilated right triangle: \(1500\) units²